This sounds like an incorrect declaration of the particular server's security settings on your machine, which has NOTHING to do with Access. Any app would have given you the same message. Access was just the one that tried to open the file. Are you sure you didn't upgrade the workstation to WinXP? Or did your security folks have a big flap to secure some machines lately?
If this is really a security settings issue, you have to go to Internet Explorer and put that server in a different server zone. (Trusted, Local Intranet, Internet, Restricted) Which is found under the IE menu bar, Tools >> Internet Options, select Security tab. Also look up help IN I.E. about setting the security level of a particular site.
I know you didn't say you had upgraded Windows itself, but that message is not an Access-specific message. Whoever set up your machine set it up with the high security settings. (There is a high-security policy settings template that comes with one of the MS advanced security kits.) You are running afoul of the consequences of not having previously declared your intention to trust the address in question.
What bothers me is that if this is inside your intranet and has the same sub-domain name, I.E. should automatically accept it as local intranet and let it alone. By any chance is this server outside of your firewalls and does it have a different domain name than the rest of your servers behind the firewalls? (This is commonly done to create something called a DMZ machine, one which if attacked by hackers, is no loss to company security.)
You might need to consult with your site's security manager or network security manager to see what is going on here. Machine security setup in today's world is not to be taken lightly.
The reason I am harping on I.E. is because MS continues to interweave I.E. into the Windows base O/S more and more as it accesses files. I.E. is just one more interface to the cross-node data access subsystem. Which is why I'm suggesting that I.E. might be the way to fix the problem.