Mato,
Wish I had more to offer than this but it is really hard to say what the problem might be without at least a multimeter and some time...unless you are committed to getting into a project that may never resolve I'd stay away from the $150 unit. Yes, it could just be a bad connection or a bad fuse or something simple like that, but it could also be a bad logic circuit or something like that. IC logic issues creep me out.
And the thing is, if you can't get it to PLAY or REC then there's a whole HOST of functions for which you have no idea whether or not they work...what if...what if something went haywire on the PSU board and toasted a bunch of stuff downstream? You just don't know.
If you are set on a 388 you could get the $150 unit and think of it as a parts deck. If you can't get it going, then you've got a good donor machine for the right one when it comes along...and $800 is too steep IMHO. I can see paying $500 for a really nice 388 in fully-functional condition, but not much more. I paid $350 for mine and it needs a little TLC but not much, and cleaned up nice...I paid $125 for my parts 388 that was 100% complete and its only issue was a bad reel motor.
So think about that stuff before diving in, but the 388 is a wonderunit.
What's your background BTW? And welcome!