Hi Andrei;
I spend around 10 years collecting, buying, selling and repairing vintage audio hi-fi equipment. Mostly from the 70s as this was a peak of it's consumer interest (pre PC and other digital consumer products). There was lots of competition between manufactures in all price ranges and some great quality products were designed and made in that era.
Anyway the most common problem with symptoms you describe is dirty switch contacts. On a cassette deck there is usually a large multi-pole switch usually mounted on the main circuit board. It's used to switch signals from playback to record mode and can cause oscillation and noise if some of the switch contacts are dirty. The solution is usually a good cleaning with a good contact cleaner and working the switch contacts. I've saved several cassette decks with just a good cleaning of all the switch and variable pots, nothing else required. Not sure it will solve your problem but it's something pretty easy to do yourself without a large expense. True troubleshooting generally requires a O-scope, schematic and experiance in signal tracing for problem isolation, but give it a good cleaning first and see if that helps or not.
Good luck
Lefty