If your network is set to the old standard, WEP, you could have some problems. It may depend what kind of computer you have. I had to change from WEP to WLAN when I bought a new computer last summer. I had two older computers. The oldest (8 year old computer) only worked on the old WEP, the 4 year old computer could utilize WEP or WLAN, and the new one I bought last summer only worked on WLAN. I had to call my internet company so they could change me from WEP to WLAN. They didn't really want to because they'd never heard of this problem, but I got the advice from Mac. (New computer is a Mac, but I don't think it matters whether it's a Mac or PC).
After the change (from WEP) the oldest computer couldn't access the internet any longer. The new Mac was slow on the internet under old protocol (WEP), and couldn't download anything at all until changed to WLAN.
Anyway. Worth trying. Could be an easy fix.
I also second buying a new router.
Edit: I just finally located what protocol is on my new computer, and it looks like the new is WEP, the old WLAN, so...reverse the above.
Sorry, I'm not an IT. If anyone has anything to add to this. It certainly worked. Anyway, check your protocol, and have them try a different one. Sounds like exactly what worked with mine.