Give up using the braid...that stuff sucks (or, rather, it doesn't).
Get yourself a solder sucker if you're going to do stuff like this.

BTW, if I had an audio power amp that didn't work, I think the caps
would be near the end of my list of things to check. Start with the
power (aka output) transistors and work your way backwards. Unless
this is a really esoteric unit, both channels probably share the power
supply, so if one channel is working, you can probably assume that's OK.