First of all....STOP using the incorrect terminology...please!
***"Strong crank, but still won't turn over."***
CRANKING...and TURNING OVER are the same thing.
I'm sure you mean to say "Strong crank, but still won't start up and run."

Have you checked to see if a spark is occurring at the plug?
Take plug out of engine and then reconnect to the plug wire.
Lay the plug on a bare metal surface of the engine where you will be able to see the plug electrodes. Crank the engine and watch for an nice bright bluish white spark.

Did you replace the battery with an exact same physical size and capacity replacement? Same CCA?

Take you new battery and have it load tested to see if it is good. More likely than not it isn't.

Clarification: when I turn the key, the engine cranks but never starts to run.

Mownie, I will try your suggestion and check for spark.

Justalurker, I replaced the battery with the top end Sears Die Hard Gold tractor battery. 340 CCA. I don't know what the CCA on the original JD battery, but I presume it was no more than on this Die Hard.

And you're also presuming that you got a new battery that was good.

Take the battery back to sears and have them load test it in front of you. You wouldn't believe how many wet cell batteries are sold that have a defective cell.

You are correct that the safety interlocks of the X304 would stop it from cranking.

How long has it been since you last started the X304 till it would not start?

Is the X304 stored outside where mice might get to the engine?

Mownie, I tried to check for a spark on the spark plug. Presuming I did this correctly, I did not see a spark generate on either side.

Justalurker,
I've been trying to make the mower run for the last two days. The last time it was running was a about 3-4 weeks ago. The mower is stored in the garage where it is cold but covered. There are no signs of mice or rodents in the garage.

If you have no spark, disconnect the grounding terminal that goes to the coils. If it starts and runs, then you will have to troubleshoot the safety/ control system. AN FYI- I've seen repeated ECU's fail on units that have loose battery cables.

What tomplum said.......about disconnecting the kill wire from the coils.
I believe the seat switch will not inhibit the starter from cranking, but it will kill the spark.

i am hoping to find the grounding wire under the flywheel cover (shroud?). this is a kawasaki twin engine. does that mean there are two grounding wires? not sure which wire it is on the jd parts diagram but will dig around and be back with update.

if it runs without the ground (is the ground the "kill switch"?) wire, i will direct my attention to the seat safety wiring.

thank u for your guidance.

tomplum. can you elaborate on the ECU failure you mentioned? what is ECU?

The ECU is located under the top of the dash and seems to have been a bit problematic on the X series. Most I don't think will have a problem mind you, but I have seen them fail on occaision. Earlier X300 models I believe had a recall or at least a special policy. I mentioned that I've seen a few times where battery cables were loose. One customer keeps removing the battery from his X to run his generator. Tightens the battery cables -as tight as his fingers will get the bolts. 2 ECus in 2 years on his alone. I'm not sure why this occurs for sure. There is a troubleshooting procedure in the manual which is kind of lengthy for what it is. If they all sub to the same one, I might just keep one in my tool box, just like the igniters on the old singles....

***"i am hoping to find the grounding wire under the flywheel cover (shroud?)"***
Yes, that is where the wire is connected to the magneto coils.
***"kawasaki twin engine. does that mean there are two grounding wires?"***
Yes, 2 connections, one per coil. Essentially it is one wire having a connector terminal for each coil. Beware that with the flywheel cover removed, cooling air will not be ducted to the heads and cylinders, so if it does run with kill wires removed from the mags, don't run it very long like that.

did some searches on the internet. found this post which is similar to my experience. i also tried to jump my battery with a starter set to 200A and did the incorrect connection pos to pos and neg to neg rather than neg to engine block.

i believe the problem is going to be at the ECU like tomplum said.

since the all the safeties (seat, PTO, and brake) prevent the engine from cranking and the engine does crank, i'm thinking its probably not the safety switches.'

so i'm gonna skip to just changing the ECU for a new one. local dealer has one.

will update you.

won't let me post the link to the other site where someone reported a similar problem and successful solution.

Success. Installed new ECU and it started right up.

Tomplum and Mownie, thank you very much for your help. Much appreciated.

Additional comment: Other forums have recommended removing the battery cables before charging. They also recommend avoid jumping the tractor, though there is a section in the JD manual that gives instruction on using a booster battery.

I suspect my ECU was fried by the mere act of jumping it or because i connected pos to pos and neg to neg as opposed to neg to ground.

***"I suspect my ECU was fried by the mere act of jumping it or because i connected pos to pos and neg to neg as opposed to neg to ground."***
NO! Whether you connect directly to the battery posts with both cables (whether charger leads or booster cables) makes no difference to the ECU (electrically speaking).
The instructions telling you to connect the negative lead to a good ground on the engine is for YOUR SAFETY, not for the machine's welfare.
The instructions are actually a sequential set of steps to perform in a SPECIFIC order that will prevent the battery from exploding due to an arc/spark that occurs when the LAST cable connection is made.
By making the last connecting point somewhere away from the battery per se, you deny the explosive battery gases a source of ignition.
If you inadvertently left the key switch of the X 304 turned on when you were making your jumper connections, that might have caused a problem similar to what tomplum has observed with finger tight battery terminal bolts.

mownie,
oh i see. thats helpful to know. i always connect neg to something other than neg terminal when i jump cars, but in this case, there was nothing really convenient to hook it to. i regret that decision now :)

i was at the JD dealer and he was telling me a story how a battery blew up and burned the face of one of his workers. he said at the very least, always where eye protection when working with battery.

the ignition key was in the off position when i jumped it. it would be nice to know how to avoid having to replace the ECU in the future should i have another battery issue.

otherwise, to avoid the problem at all, i think i'm not going to jump the mower. i'll just remove the battery and charge. in that case, how would you hook up the battery charger to the disconnected battery? pos to pos and neg to what?

Glad that you are up and running. Maybe the 200A boost cycle of the charger was a bit much all things considered. I really don't know how accurate they are or how much of a surge there may be. The same trend has occured in the single cylinder Kaws with the single pole igniter failures. Mind you, there isn't even 12 volts that even hit that circuit. Yet, when you find the guy that has a failed igniter- maybe his second was the guy that regularly started the thing witha big booster. Obviously not always- but there seems to be a correlation.

***"how would you hook up the battery charger to the disconnected battery? pos to pos and neg to what?"***
You connect pos to pos, then neg to neg........then you plug the battery charger in to an A/C power outlet and later when the battery is charged, you unplug the charger from the A/C outlet and disconnect the charger cables.........in that order.

mownie,
thanks for your advice on the battery charging.
rid