That is very likely precisely the problem ... but not from just 1 capacitor.
Upon inspection, you're probably going to find that multiple capacitors have failed, and that dismantling this unit is a PITA. Not as bad as a Panasonic, but still about as much fun as going to the dentist. Sourcing replacements isn't always easy to do.
Now, don't get me wrong. Quality VCRs are always worth repairing, or selling for parts, never trashing/recycling. Because it surely does have other parts still in good condition.
But I've also never been fond of the D-VHS decks, because they are tuned to SP mode, and the LP/EP tracking can be pretty bad. The 30000 model specifically has never been a well-liked machine, with DVHS kudos mostly going to the 40000. With that many tapes left to go, I would be amazed if you can get that specific machine to work well with all of them, or even a majority.
So ask yourself this question: In the past 2 years, how many tapes has it cooperated perfectly with? And how many were not SP mode? That should help you decide on getting it fixed, vs getting another...
... or better yet, do both, get it fixed AND get another deck. There's a reason that hobby/pro veterans have multiple VCRs. And it's not because we like collecting them!
Whatever you decide, (a) the VCR is not garbage, don't trash it, (b) we'll try to help you.