What does no chime on boot mean?
You don't specify how old your MBP is, but some MBPs built a few years ago shipped with graphics cards that fatally crashed after a few years of years. That's what happened to mine and it was a warranty fix because a recall was done.

My understanding of the chime is that it is hard-coded into the motherboard. If it is not playing with the chime, then you probably have something wrong down to that level. It may be a simple fix, it may not, but only Apple will be able to tell you definitively.

(Answer edited per comments)