You aren't going to get shocked. Just pull the back of the case completely off. So long as you don't start fondling the red flyback wire and suction cup with your bare fingers, stroking it like a dog, you will be okay. Yes, I've opened these old Macs dozens of times myself, both as a hobbyist and when I worked as a service tech in the late 1980's.

You will not be able to spot many bad capacitors simply by looking at them. But a bad cap is highly unlikely to cause a RAM error, so don't worry about that.

I personally would take time to disconnect and then reconnect all the connectors you see (leave the suction cup of the flyback alone though). Floppy drive connectors, analog board connectors, logic board connector -- reseat them all. If there is a lot of dust on the logic board, then remove the board and blow it off, then put it back and reconnect. Maybe shoot us some photos of the insides while you do this.