Buy a new 252 toro valve and replace all the the top and internal parts. Almost certain the problem you have is the diaphram is bad but the cost of a new valve is about the same as the cost of a diaphram and coil so just get a new one. ALL the new parts will work with the old valve. The metal bands are to help keep the female threads from splitting.

Make sure you check your valve boxes out in the yard. It almost sounds like you could have the drain left open (if your boxes are flooded) ... which needs to be shut. Or it is possible that when someone winterized it, that one or more valves were left open (on). Also, sometimes a valve can be manualy left on ... so I usually make sure all the value are turned off (the manual control is off, has nothing to do with the controller signals). Normally, the valves all turn to the left for manual off. Are you getting water coming out the backflow manifold( the part usually on the outside wall of the house) ? Sometimes you need to replace a plunger there, if you activated the system too early or had it otherwise freeze up during the winter.

If this valve is 22 years old then it is probably the solenoid plunger that has rusted or something in the solenoid's connection to the valve. The solenoid is there but is not opening the valve properly. It's probably time to change out the whole valve. I would clean it out and if that doesn't work, have it changed out completely.

A multimeter is a handheld tool used to check the function of the timer and wiring. They are less than or around $10 at the hardware store. They usually have a dial and digital screen. If you can obtain one, they are very simple to use, and good if you are trying to avoid a house call. Do you think you could obtain one? You probably have the Irritrol Total Control 18. Re-programming is when you turn the dial to the different items and set your stations, run times, current day, time, etc. When you remove the battery and power, often times this will reset that controller and it will be necessary to reprogram your stations.