Were you using a purchased license with the Personal Edition you were using before? eEye may have reset it for you if you are. You can't use it with the BETA anyways, but thought I would ask.
Since your installation is already messed up, I would first disable the current installation of Blink that you have on your system now. To do this:
Start >> Run >> type "msconfig" >> select the Startup Tab. Uncheck the box next to Blink and then restart your system.
You may try uninstalling it again at this point OR simply try installing the new BETA 4.5.0 (which does work with Windows 7) over top of it. It may fix up any of the files that are corrupted allowing you to uninstall it completely.
http://forums.eeye.com/forums/t/1152.aspx
I would also recommend using a free program like CCleaner to clean up your system too (if you have not already done so):
http://forums.eeye.com/forums/t/752.aspx