Since your company network uses static addresses, you need to assign the router an address from your network. For example ... your default address of the router is probably 192.168.1.1 (or similar). Suppose your company network range is using 10.1.1.x, you will need to manually specify your router as something like 10.1.1.254 (if its not in use by another pc - check with a pc already on the network and ping for an address to use). Another way to describe what you need to do is this: assign the router's WAN address an address from your network. Look for this option in your router web interface.
From your earlier comments ... this wireless router is being put into service to allow wireless pc's internet access, but not necessarily access to your various network resources ... correct? Then you will want to have your router continue running DHCP server. I'd suggest slightly changing the ip address scope from (assuming) 192.168.1.1-150 to something like 192.168.55.100-250. Just a security precaution ... mix things up a little bit ... hackers know factory defaults.
Ill try to find some screen shots of where you need to assign the WAN address in the router's web interface.
***Since I cant add pictures or attachments ... here's what I found in the manual (if I got the right one for the WGT624?) on page 3-4 of the manual is a screenshot that shows where you manually input your static ip address, subnet mask and default gateway in the Internet IP Address box. De-select "Get Dynamically from ISP" and put this info in ... exactly as you would for another pc on your network. Once this is done, you should be able to get out to the internet.