Qsys doesn't open

You should provide more information. What version are you running? What OS? Have you checked task manager (alt ctrl del or ctrl shift esc). Have you checked your resource manager (Win7: from Task mgr, Performance Tab, Resource Monitor Button] to see if Qsys is chugging away at something?

Altera generates a few different debug logs located in the altera/[version]/[program] directory. See if you can find one for Qsys or Quartus II.

Does your software point to a license file (free or paid)? Has that license file (or server) moved/changed? Quartus II started running very slow for me. It was the free version but I had a license still which was pointing to a server that was moved and wasn't working anymore. Quartus took 10 minutes to compile a 1 minute project.