Modem problem???

I have 2 Acer Aspire Desktop with Vista Home Premium and an old pentium 2 Gateway with Windows XP. My Acer is connected to the internet through a Netgear WGT624 Router which is connected to my Road Runner modem. The Gateway computer has a wireless internet connection. I couldn't get Vista to start up and my keyboard and mouse wouldn't work so I ended up taking the Acer to be worked on. I hooked my Gateway up to the Netgear Router and it worked fine at first then it started having the same problem as the Acer. I then decided to take the router off and connect the computer directly to the Road Runner modem. It started out acting fine then began to have the same problem again. At that point I decided to put the Gateway computer back where it had been and it is now working fine with the wireless internet connection. I am baffled as to what is going on. The only thing I can figure it that there may be a problem with the modem since both computers had the same problem when attached to the modem. ?????