Youve prolly already done this but the first thing I would do is turn everything off, the modem, router, 360's, PC, everything. Then turn back on modem first, reset the router back to factory defaults (if you dont have any fancy port forwarding or permission setting or filters, if you do make sure you know what to put back in before erasing it all), then each individual component. Check and make sure the router has the latest Firmware also, it might help solve some issues.
You could go in the router settings and bind the MAC address of each component to an IP, and turn off DHCP. Or maybe change the IP range the DHCP is going to give out IP's. With my router its IP is 192.168.1.1, but I have the DHCP IP range set to 192.168.1.100-150
Try putting the components in the DMZ one at a time, see if that makes a difference, maybe the NAT firewall is interfering with something. The MTU is set to Auto on mine, but the big CISCO routers we work on in class have their MTU set to 1500 all the time.
I dont know what kind yours is but I used to have a D-Link WBR 2310 wireless router and it was a P.O.S to be honest. It dropped connection, was slow as hell sometimes, and would randomly reset itself. Once I got this WRT54G I havent had 1 single problem with it.
Or like you say, if its an old router, maybe it has just plain had the biscuit, and a new router might be in order. I'm sure you can pick one up for about 50 bucks, or even less if you want a used one off Ebay.
Ive got one of
THESE and it works great. If you are looking to buy another one I would highly recommend it.
Good Luck!