This problem, and the "could not complete the requested operation" error, are often memory issues. It may go away if you close some stuff. I've also seen it fixed by just reducing the total number of fonts (if you have thousands), and by deleting the illustrator preferences file, or removing the plugins and then moving them back 1 by 1 until you find a bad plugin.
The easiest way to isolate a crap font is the half'n'half trial and error method. By which I mean:
Copy all the fonts you want into a backup folder.
Delete all fonts except system fonts in the system font folder.
Highlight about 50% of the fonts in the backup folder and copy them to the system font folder. Start illustrator. If it crashes, you know the bad font is somewhere in that group.
If it doesn't, it's probably in the other 50%. Make a new folder for the "suspect fonts" in your backup (call it badfonts or whatever) and paste the bad half into there.
Now delete everything you just copied into the system font folder (so it's clean again), and go to the badfonts folder, and highlight half of those, and paste into the system folder, see if illustrator starts... pretty much repeat the stuff before, except now you're narrowing it down to 1/4th of your possible fonts. Then repeat again and narrow to 1/8th, 1/16th, and so on, until you have one bad font.
It sounds lame and tedious but it really is the fastest way to isolate one bad font or group of fonts. And it's not that bad, I can do it in maybe 15 minutes (and I've had to before). If you paste in half and illustrator starts, and then paste in the other half and illustrator still starts, that tells you the problem isn't one particular font, but just the large number of fonts it has to keep loaded in memory.