I used to do this for a living and can probably help you.
It sounds like you’re describing the manifold, where all the lines from the various zones come together in a valve box with the electric valves and tie into a live line. (I’m guessing here, because I can’t see it IRL.)
First off, while it’s probably disconcerting to see the manifold for a new sprinkler system completely under water, this won’t likely harm your electric valves.
Check the valves themselves. One might have an open or busted bleed screw. You should see plastic screws somewhere in the vicinity of the electric solenoids. Make sure they’re tight and not leaking.
Now, for the bigger problem. Manifolds are a pain in the ass to repair, because of the difficulty you described. If a manifold tee springs a leak, often the valve box has to be dug up, the individual lines have to be cut after the electric valves, and most of the manifold will have to be disconnected from the live line.
Let me say that there’s no reason why your irrigation installer should have glued the manifold tees together. Most of the manifold tees I’ve seen thread together and teflon tape or paste keeps the threads tight. Now your whole manifold likely has to come out of the ground.
Shut off the water. Dig up the valve box. Then, dig back each individual line at least two feet and cut the poly pipe after the electric valve. Disconnect the live line leading into the manifold (you may have to cut this if the fitting is glued or you otherwise can’t turn the manifold). Once you have the manifold out of the ground, get rid of the crappy glued manifold tees and rebuild the manifold using threaded tees and some teflon tape or paste. Couple everything back together, using the appropriate couplings. (You didn’t say whether the line leading to the manifold was PVC, copper or what have you…) Couple the individual lines with insert couplings and squeeze clamps.
Sorry that this is probably the only solution that can help you. It’s probably a couple hours of labor, depending on how many zones you have and how much room you have to work. On the positive side, it shouldn’t cost you more than $20 in materials. Trust me - I’ve tried every kind of stop-leak there is to repair manifold leaks. Repairs rarely last more than a couple days. If it were me, I’d rebuild this thing, ensuring it will give you years of reliable service.