Assuming this isn't anything obvious it could be any number of things. Couple of things to try that might help provide some more information:
Try to ping the server from the client and see if you get a reply. If that fails you've got a network issue - anything from switch, to router to DNS server might be part of the issue:
Another place to look is the event viewer - open Control Panel->Adminstrative Tools->Event Viewer. Once opened look in Applications and Services Logs->Miner and see if any error type event is logged which might help narrow down where to look.
We have the issue sorted out. Its hard to know exactly what caused it as the user had done a system restore of his Windows 7 laptop as he had suspected a problem with recent Windows updates. After i talked to him, he found a previous email where he had the similiar problem and deleted the default domain path folders in his C:\Users\userid\AppData\Local\ESRI folder that contain ESRI configuration information. This along with an ArcFM reinstall (which most likely wasn't required) resolved his previous issue.
Yesterday, ArcMap was till crashing after we set arcFM to no products in the license manager. He followed the steps in this post to remove his ESRI customizations. We had tried copying the ESRI folder fropm anothe ruser profile on the same machine that the user could log in which didn't work.
INDENT]1) Delete (or rename) these per user folders for ArcGIS on the system:
[INDENT]C:\Documents and Settings\<user name>\My Documents\ArcGIS\
(copy out any MXD, projections or Geodatabase located here that you want to keep)
C:\Documents and Settings\<user name>\Application Data\ESRI\[/INDENT]
( Note: it would be C:\Users\<user name>\My Documents\ArcGIS\ and C:\Users\<user name>\AppData\Roaming\ESRI\ on Windows 7 or Vista )
2) Open regedit, navigate down the HKEY_CURRENT_USER key opening each "+";
[INDENT]delete the HKEY_CURRENT_USER\Software\ESRI Key from the registry.[/INDENT]
( Note: changes to the registry are immediate and irrevocable, so be careful with each edit )
Log out and back in.
He is in the middle of finishing off the reinstall, but he can get an ArcFM license now and ArcMap runs fine.