I have reinstalled FB many times on my machine and on each installation after a while Flash Builder stops opening. I keep my task manager open to see what's going on but the process doesn't seem to start, or if it does, it closes immediatly. Where can I see the error log? I can start Flash Builder normally if I use FlashBuilderC.exe
This may very well not be your problem, but after I downloaded FB 4.7 and messed with some things I had this same issue (Windows 7).
Turns out it was looking for the last workspace it used (since I don't have "Ask for workspace on startup" checked) and because I moved the folder, it couldn't find it. As a result, I'd see the process pop up in Task Manager, sit there a bit, then peace out.