Here are the First two things to check.
1.) Space Available; is there any space left where the Exchange Databases are? If not free up some space!
2.) Has the database hit its Limit? For Exchange 2003 its 75GB (with the registry modification)
If it’s neither of these you have to start looking at the domain as a whole.
Remember that EVERYTHING is tied together, if Exchange isn’t working, it could very well be a Domain Controller issue!
First thing to do would be to run a DCDiag, if this fails you have issues. The most likely cause would be the Netlogon service is paused or stopped. Restart it, and then restart the exchange Server. Re-run DCDiag to verify that all is well
If none of the above solutions help, the database could be corrupt, wherein you would have to utilize eseutil to find out of the DB is in fact corrupt. At that point let’s hope you have good backups be it Veeam, Backup Exec, or Windows Server Backups.