Probably some capacitor or transistor blew up. Have a good look around and you should find something that looks brunt or burst open.
There's way easier circuits to try learning electronics from. But if you have lots of time and are interested enough, I would say don't plug it in, just get a multi-meter, and start at the cord, and start making a map of what is connected to what. That will turn into a rats nests of connections in no time, so I'd read up on the basics of linear power supplies, I'm guessing this has 1. There's capacitor's that can still be dangerous for a while after it's unplugged too. Again, there's a ton of safety stuff you really should read up on.
Basically the power comes in on the cord, there's probably a fuse, then a step-down transformer to lower the 120VAC to maybe 24 or 48VAC as an example. Then a full-wave rectifier that basically turns the negative voltage portions of the AC sinewave into all positive voltage portions of a sinewave. For 120VAC in, the rectifier is usually followed by big capacitors, that will charge up to about a steady 170VDC. Besides a few added parts and things, like maybe some smaller standby power supply section, most all power supplies with a transformer, will be pretty similar up to there.
And if you know some basics, you can get pretty far into a power supply, with it unplugged and just a DMM, and rule out a lot of parts, or be fairly sure they are ok. If you have a soldering iron, you can remove a lot of parts are really check them out.
Then from that 170VDC, then it starts branching out to circuits that make other voltage levels/rails, and down to circuits that do VCR stuff.
I'm forgetting about the step-down transformer, so you probably won't find 170VDC on a VCR.
There's a lot of safety considerations, and anything with 120V or 240V is very dangerous, like walking along a cliff edge in the dark.
Just trying to probe solder joints with a DMM, can be tricky, the probes can slide off the solder pretty easily, and sometimes you use a lot of pressure too. So if the device is powered, it's pretty easily for your hand or the probe to slip and hit something else.
I'd really recommend against probing stuff with it plugged in, there's way way easier and safer things play with if you want to learn some EE that bad.