I feel honor-bound to issue the obligatory warning that circumventing the local security measures could totally wreck your IT career and suggest you set your sights on some online time-waster that isnt risky & doesnt require extensive setup. Personally, I bring a book to work for those slack times when I'm just a warm body monitoring the systems - there, now I feel better
Rules for t/s'ing network issues - move up the OSI model & move from simple to complex. Dont assume connection point a goes through the same devices as connection point b - even though they may be next to each other physically.
1) Verify that your setup works from a simple, known topology.
2) Learn all you reasonably can about the topology at your workplace, otherwise you can waste a lot of time guessing.
3) Duplicate the working setup on your laptop.
3a) Once 3 works, point the client to your server - if this works, your server is verified, if not modify server settings until it does.
3b) Once 3a works, substitute your client, and modify settings until it works.
4) If 3 doesnt work, it's likely the underlying platform (os, other installed programs, etc). SP2 did fix some things in the XP network kernel, so I would suspect this first.
5) Verify (as far a possible) that you & your co-worker have the same level of access through any internal security (VPN, firewalls, etc).