Hi Kevin,
Sorry this reply is not more specific but ...
There are many questions from a networking perspective that are still unanswered (and in some cases unasked) here. However, based on the fact that you are saying that everything worked well up until 2-3 weeks ago, one of the most important would be - What changed ?
In thinking about the changes, you have to consider Hardware (Servers, Clients and Hubs/Switches even cabling) and Software and with Software you have to consider all Software - Adagio, O/S, and other Apps (especially Anti-Virus and/or Spyware Background/On-Access/Real-Time scanners).
Troubleshooting network related problems can be exceptionally difficult to track down. When you say that other programs are working fine, bear in mind that Adagio is much more taxing on a network than say Word or Excel. In fact, in many instances, no other application is more taxing on the network than the accounting app.
Personally, I think that you need to get some direct assistance on this one. Where a much closer look can be taken at your Network. Is it Peer-to-Peer or Client Server ? Is your server as old as the Windows 98 PCs ? Are you running at 10, 100 or 1000 Mbps ? You still haven't given us an idea of your database size ? Number of Customers etc. ?
You should definitely move to the new Win XP PCs and get everything working well in the new environment BEFORE attempting any Adagio Upgrades. I believe there's a better than 70% chance that this alone will provide major speed improvements.
Not doing the Upgrade yourself is not really a matter whether they are problems with the upgrade, it's to do with the fact that being a major upgrade there are many new features and an AC can help you configure the product to get the best results from the Upgrade. However, if going it on your own, please ensure that all of your modules are at the right versions for compatibility.
Good Luck !!!
Pete