So,
I desoldered the capacitor that was previously heating up and checked it with an ohmmeter—everything looked good. I reinstalled it and then desoldered those burnt MOSFETs (which wasn't easy, by the way).
After reassembling everything, it worked! However, I noticed that both circuits for the main motors are heating up slightly, the current might be too high by design. Not sure how long it’ll keep working, but we'll see. I have some spares ready for replacement if needed.

As for the power input circuit, I left a 20V MOSFET in place because it's working fine and isn't heating up, so I decided not to touch it for now.
Thank you for your help!