You have a heap of work to do before you can reinstall it. NEVER try to get rid of PSE by putting it in the trash. You must use the uninstaller. By attempting to trash it you just made a big old mess for yourself.
You will need to download and run this:
Then go through your hard drive and manually dig out and trash all the bits you can find. Pay special attention to the library at the top of your hard drive>Application Support>Adobe.
Once you successfully get that cleaned up, you can try reinstalling.
You can download PSE 11 here, but you must follow the Very Important Instructions exactly, even when they don't seem to make much sense, or it won't work: