Well, the accelerator shouldn't be having an effect on the picture at all, except for some tearing / glitching issues some people have with certain accelerator / motherboard combinations. Capacitors are quite a likely culprit - even if they haven't failed totally in the average quality one, they could still have degraded enough to cause poor signal quality. Or, one might have failed which wasn't critical, but just helped reduce noise or decouble or something. It's also possible that the power supply is causing a funny noise effect - I had that myself using a PicoPSU and cheap laptop charger. Changed to a better quality one and the picture was crystal clear. The original Amiga power supplies are getting old as well, and they also contain lots of capacitors for smoothing the power and eliminating noise.
Edit: Good point Bloodline, I guess different accelerators could be introducing noise in different ways which cause video issues... Would be interesting to swap them over, and the PSUs, and see if it's linked to either.