Did you replace the burnt caps? I'm a little unclear on what you're asking with those (C8/C6).
For C3 - do you still have a piece of the lead stuck in there? It looks like you may have taken the solder point off with all of the heat, which could mean that even if you get the remainder of the lead out that you may not be able to solder it, and if it does solder, it may not make a connection with the trace in the board.
If that is what happened (I'm not sure that it is as I can't see the hole all that well) you can likely still use the board but may have to jumper it (whatever you do, don't bin it! once the problem is found someone here can most likely help you find a fix). C3 goes to R3 and to ground, but that's as confident as I can be looking at a schematic right now, you'll need someone with more experience than me to tell you which pad to jump to if that is what's needed.
When you're de-soldering, if you don't get it the first 2 or so times, let it cool off for a while before getting back to it. These things heat up incredibly quickly and they take a while to dissipate that heat. Take a shot at de-soldering, if it doesn't work, do something else for a little bit and give it another shot. Patience is your friend here.
You'll get a feel for what works for you and the more you do it the better you will get. Someone will drop in who is (much) more knowledgeable than I am and be able to point you in the right direction. Keep it up, dude.
Edit to add: It also looks like IC1 in the first photo is in upside down. If you've powered it up you will probably have to replace it.