Thanks for the suggestion, roky, but those didn't work.
However, I DID happen to find out why Flash 11.2 wasn't working on my system.
Turns out Flash 11.2 in Linux requires the SSE2 extensions on the CPU. Since my CPU is old (Athlon XP 3200+), it did not have these.
I uninstalled 11.2 and installed 10.3 through the Synaptic Package Manager. I am actually able to see YouTube videos now. My CPU usage is around 90% when I watch a video but at least I can.
Cool. I guess I can consider this solved. I will have to figure out how to mark it as such.