Anything over 60 seconds for application launch suggests a problem.
Problems with plugins or fonts are common causes of launch slow-down. Which processes are occurring when the delay happens? Have you moved any plugins or font collections recently?
Your disks are full, I'd say. Check the AE prefs and clean out the Media Cache. Startup takes forever, because AE is looking up and veryfying each single file in the cache. If you never changed it, it defaults to C:\Documents and Settings\You\Application Data\Adobe on Windows XP for instance. If you look it up, you surely wil lsee several gigabytes of files In addition, do some generic system maintenance by ways of CCleaner and defragmenting your drive. also look for auto-saves, render logs and other stuff. Of course Andrew is also right - flakey fonts, CoDecs and even modified graphics card settings can sometimes have the weirdest side effects on system health....
You may also have a corrupted font or some bad memory. Did this problem just start?