Time to source a service manual, and start tracing audio path with (preferrably) a scope. In consumer stuff, it's likely that the bias oscillator serves both the erase and record functions. They may have different amplifiers/setting points, though.
Once you get a manual with block diagram, you can evaluate what circuit elements are ok. For example, if you input a signal, enter record/pause, and monitor the output jacks, you're in EE mode -- electronics-to-electronics. If this sounds good and responds to input level control adjustments, then that will tell you that certain circuit elements are fine, which would mean the problem is in the 'head amp' part -- the circuit that takes the input and applies EQ, bias, and drive level to the record head. You can actually monitor the connections on the record head to see if the head amp is doing its job, but it's not going to 'sound' like good audio -- it'll have an EQ curve applied, plus bias that your test monitoring will need to deal with. This is why it's best to have a maintenance manual/schematic before digging in.
I've never done it, but you might be able to use a car cassette adaptor to suss out some info. You know, the $6 things you use to get your iPhone to play thru your cassette deck. It's essentially a tape head connected to a headphone jack, with some EQ thrown in. Used in reverse, the head would pick up the varying magnetic flux from a 'recording' head on your deck, and make it available as an output on the headphone jack. Level and EQ issues will abound, but it will tell you if the signal is getting to the record head in the deck. I'm going to guess (and it's only a guess) that if it sounds 'ungarbled' using this method, then the bias source, amp, or mixer is at fault in the deck.
I'm also assuming it's not your actual tape that's at fault, and that you've tried recording on other tapes with the same bad results...
I notice it's a three-head deck. You should also verify the switching and circuitry is good in the monitor source path. There should be a switch along the lines of 'monitor input' vs. 'monitor tape playback'. Because three heads let you record, then immediately play back 1/8" later. Since playback works OK, that uses the majority of the 'monitor tape playback' circuit. But things could go awry in the logic switching of monitoring sources.
