You have several options.

1. Put a rebuild kit in the existing valves.

2. Yes, new valves are a definite possibility. Those look to be screw connections to the valves and flow controls (the hexes for a wrench give it away), so the pipe unions could be unscrewed, the assembly removed and taken apart and then new valves and flow controls installed. Shut off the water first, and don't install with the piping reversed! You will probably need some big slip joint pliers or pipe wrenches to get those pipe unions loose!

https://www.amazon.com/Orbit-57623-FPT-Anti-Siphon-Valve/dp/B00004S1V6/ref=sr_1_2?crid=2T2D7MXF7QAZH&keywords=sprinkler+valves+3%2F4+inch&qid=1654783251&sprefix=Sprinkler+Valves%2Caps%2C106&sr=8-2

3. If all else fails, cut off the vertical PVC pipes below the pipe unions and replace everything with new. It's DIYable.

If you want to go back to automatic controls, there are basic multi-zone controllers available for less than $100:

https://www.amazon.com/Rain-Bird-SST600IN-Irrigation-6-Station/dp/B071D7TSRH/ref=sr_1_5?c=ts&keywords=Automatic+Irrigation+Controllers&qid=1654783607&refinements=p_89%3ARain+Bird&rnid=2528832011&s=lawn-garden&sr=1-5&ts_id=3480701011

Don't even fool with the old battery operated controller, go new, operating from a 120V to 24v wall adapter. All the valves that work with these controllers operate from 24v AC, so make sure new valves or solenoids work with that. No electrician needed, just a 24v hot wire to each valve and a common neutral wire, multi-wire thermostat cable cut to length from Lowe's works fine.

Where exactly is the leak coming from with the Richdel? Are you sure it's the valve body itself and not one of the joints?

Just double checked. It's coming from multiple places. Under the black thing I turn to open it up/turn sprinklers on (still not sure if that's called a solenoid or not) it's leaking; can't tighten it enough to get it to stop seeping. It also looks like some water is seeping out on the top of the valve body where the screws are attached to a metal ring, as well as on the side as well as right where the thing meets the pipe. Assuming it's a goner....

Yes, you've diagnosed it correctly as a goner. So, if that was my setup, and assuming the pipes are intact, I'd replace both valves. Start by turning off the water to them. Then you can uninstall them by unscrewing the blue fittings that are located a couple of inches below each valve. Those pieces are called unions and allow you to easily take things like this apart (unless the previous owner did something goofy, like glued part of it). It might take a bit of force to unscrew them after all this time, but a pair of large, slip joint pliers should do the job. If you want to, you could then get a cap for the supply pipe going to each of the valves so you can turn the supply back on if you need to for other purposes while you refurbish everything. Valve replacements are not expensive, but the inlet and outlet spacing may be different on new valves, so it's possible you may need to do some cutting and modification to the PVC tubing to match it. It may not be possible to salvage the old unions, so you may need some new ones; however, once you get the valves demounted, you may be able to unscrew the top part of the unions from the undersides of the old valves; if so, you can possibly reuse them.

Hope that helps. Post if you have more questions.