Sony Betamax Model SL-5100 need some information

[Captainclock]

Hello everyone, I just got from a friend of mine to work on for him a 1982 vintage Betamax player/recorder that was refusing to load a tape properly (which it turned out to be a bad belt in the loading mechanism) anyways I have an old Betamax tape that I had inherited with my old Sony Hi-Fi Betamax VCR that I got from Goodwill and that Betamax Machine was from I think the mid 1980s or so but anyways this Betamax machine I'm working on seems to be able to record in βII and βIII but it seems it can only playback in βI, which kind of confuses me because if it can only playback in βI but not in βII or βIII then what's the point of the machine recording in βII or βIII if it can't play those speeds back? Which leads me to my question, concerning my inherited Betamax tape that is also my test tape, I went to play the tape in the aforementioned machine I'm working on to test it to see if it was functioning properly and all I get is a monochome picture that doesn't play at the right speed, am I to assume that the momochrome playback and wrong playback speed has to do with the fact that the tape was recorded in a speed that this machine can't handle? and if so am I to assume that I now have the machine fixed now seeing as I had the belt it needed for the loading mechanism to get the tape to load properly now?

UPDATE: I apparently read online somewhere that this particular model of Betamax machine had issues with bad electrolytic capacitors in the service board which is what's causing the VCR's playback issues, but my question is, which board is the service board on this machine? I'm assuming its one of the 2 boards on the bottom of the machine but as to which board it is I'm unsure of, so with this in mind completely disregard my question and comments reguarding the VCR's Playback speeds because I also found out that this machine indeed does playback all three Beta speeds (βI, βII, and βIII) but only records in βII and βIII.