You did not actually delete Illustrator? Did you?
You have to use the uninstaller you do not simply delete it or any other application except if it is the only option and for Illustrator you need to use the uninstaller.
You will probably have to yuuse the clean up script which you get from the Adobe site.
You have deleted Illustrator and going to run the cleanscript then make sure before running clean script you remove all adobe product because I beleive you haven't removed photoshop and it may cause issue in uninstallation after you run the clean script.
Follow the steps:-
1) Remove the complete suite using the uninstaller :-
Win;- Go to control panel and uninstall
Mac:- Mac HD-->Applications-->Utilities-->Adobe Installers
2) Run teh cleanscript
3) Create a new user account and then install
---it will be better if you let us know the version of Illustrator , photoshop and the Operating system you are using.