If your system isn't shutting itself off, you likely haven't done any damage at this point. The newer processors and gpus are very good at protecting themselves, and the remaining heatpads will still work, just not very well.
I would get some Arctic Silver 5 from Newegg.com or a local shop if someone carries it, and apply it to the cpu, the main gpu chips (the memory on the gpus need the thick heatpad, and it can be reused) and the SLI chipset that is part of the gpu heatsink assembly. Follow the directions on Arctic Silver 5 website, or aaronjb's excellent tutorial with pictures stickied in the mobile section.
The heatpads likely looked dried out as that's what they're supposed to do. When installed, they're sticky, but after a few heatcycles they firm up and dry out a little as they develop a harder interface between the chip and heatsink. Once that interface is broken, it won't reset, though it will continue to work somewhat.
As for the warranty, AW does give people permission to install it that are having heat issues. It's up to you whether you want to call them and let them know you want to install it. If you tell them you're having heat issues and you'd like to install AS5, they'll likely say go ahead.
I just installed it without notifying them as I don't anticipate it being an issue, but if you're worried about your warranty you should consider calling them and letting them know. I saw my cpu drop about 5 degrees across the board, and the gpus run cooler also. Since you were having heat issues, you'll likely see your temps drop after AS5.
For the future, you can clean the fan and blow the dust out of the radiator without removing the heatsinks. It's tight, but it can be done.