I've ran into this with individual applications over the years, and can typically solve it with either a permission repair or reinstalling the app. Today I ran into this for ALL applications for a user. You couldn't run Terminal, Safari, Disk Utility... The only thing that appeared to be ok was Finder.
I logged into another account on the machine and everything worked fine. I ran the usual disk utility commands, but no luck fixing the issue. Then I created a new account and logged in, and that account was ok too. That made me expect user profile corruption. I backed up the files, deleted the user account, then set it up again. First login and the same problem, the entire dock was question marks and nothing would run. Whatever the issue, it appeared to be directly related to this user account, but wasn't in the profile.
After wasting a bunch of additional time trying to troubleshoot this, I finally ran across the answer in the MacRumors.com forum (thank you jpete for posting it). The system folders, specifically /var/folders/, contain some cache files from user accounts. What I found is that each folder is specific to a user account, and that user account may or may not still exist in Users & Accounts. Almost like a secondary user profile area that persists even after the account has been removed. This is where the problem was. I found the folder related to the user experiencing issues by using Get Info to see who the owner of the folder was, then went into the folder named 0 (that's a zero) and deleted all the contents that it would allow me to. After rebooting I was able to login with that user account and everything was working again.
The easiest way for you to try this is to login to the account having issues and then go to Finder->Go->Go to Folder. In there type /var/folders/, then it'll open in Finder. Now go into each of the two-character folders one by one and do Get Info on the folder it contains (long alphanumeric name) until you find one that shows the username that has problems as the owner. Once you find that, go into the long alphanumeric name folder and you should be able to access the 0 (zero), C, and T folders. Do not delete those folders themselves (not sure you can even if you tried), but go into them and delete all the contents within that the system will allow you to delete. Once done, reboot the system and try logging in. Hopefully it will show you the icons in the Dock and let you run your apps once again.
Assuming you don't have Time Machine to go back to before the problem started, if this doesn't work and you have access to a 2nd account that does work on that same Mac, your best bet is to create a new user account with a different username and move your files and settings over to it from the account that has problems. Or you could back up everything and run through an installation, cleaning the drive in the process, so you have a completely fresh start.
