Bigfish... Sigh. My ex spent way to much time there...
Look on the bottom of the laptop, any model numbers there? I'm really just trying to figure out how much ram you have, what CPU and GPU, etc. You wouldn't think it, but some of those flash games can use a lot of ram and CPU power. If you have an older single core thinkpad with little ram, that's your problem.
If you want to try some things that don't cost money, grab a good antivirus and make sure you don't have a virus on your PC. Avira, AVG, etc. You can also try upgrading your GPU drivers. (newest versions of flash is supposed to support GPU acceleration.) While you're at it make sure flash is up to date. Finally, with the laptop off and unplugged flip it over and remove the bottom panel. This should give you access to the heatsinks and fan(s). Make sure they are free of dust. See if any of that helps things run better.