Hey there Notageek

Sounds like you might have either a connection issue or an ISP issue... If you are using two different browsers and they are both timing out, then it most likely something global on your machine (like network or router settings) or something related to your ISP or the website itself. Either way it can be a tough problem to nut out!
A simple work-around might be to try using an enhanced download manager. If you are using Firefox, perhaps you can test your issue out with this - try installing
Down Load Them All. It's free, and integrates into your firefox browser easily. The main feature we are looking for here is that as a download manager it shuold maintain (mulitple) persistent connections and also resume stopped/broken downloads.
If this works - then that might fox your immediate problem and allow you to download material from that website. (it should be faster too!)
Next - to try working out what the issue is - we need to test the target website, your ISP and also your machine... independently!
1) Perhaps you can post the website so that someone the forum can try downloading a file from their and view the website. If we can, then the website works. If we can't, then it might be totally out of your hands!
2) Try another machine on your ISP/connection. This will test the ISP and the router. If you have a second machine at your home that would be ideal.. Otherwise, see if you can get a friend with a laptop to plug into your network and try downloading the same file.
3) If we can reliably download with #1 , then the last link is your machine settings. I would start looking at some global settings that affect both browsers - networking settings, hardware faults, firewalls.
I hope that helps - let us know how you go!
Cheers,
:)RG