Need more details. Windows pc or Mac? Windows XP, Vista, 7 or 8?
Modem, as you stated, could mean DSL or perhaps a cable modem. If you have XP and DSL you can try Dr. TCP and tweak your MTU, the default 1500 bytes is too large of a packet size for AT&T DSL. You can find more info on this at dslreports.com.
Also how old is your networking equipment? These newer "energy saving" power bricks which power most routers (as old as G series wifi routers), including some ATT 2Wire and some Verizon Actiontech routers have a habit of dying a slow death due to power supply capacitors swelling up internally in the power supply brick, which in turn degrades router performance. Maybe that's why your ISP is doing a modem watch.
Some games can use considerable amounts of bandwidth. If you can find a linksys wrt54gl at some used computer store, flash Tomato or DDWRT they have bandwidth graphs so you can observe - at peak game play, how much bandwidth is being used, perhaps your Internet is saturated. Hopefully you have a reasonable Internet speed - at least 3 megabit?
Since you're hardwired, you could also look at doing some tcp tuning. Windows Vista/7/8 and to a lesser extent XP are tuned very aggressively and if routers at the isp and along the way on the Internet these settings may not be optimal because you do have not control over what hops the packets make, and if one router along the way is old or overloaded can't handle the "bursty" nature of Windows packets, taming your TCP tuning for the weakest link may help.
If your PC's have an Intel based adapter (especially of a Gigabit generation) consider visiting the Intel Website for newer drivers. They will be newer than what you can get say at Dell or HP (assuming you have one of these pc's). Create a restore point before upgrading drivers. Alternately Windows Update (on Vista, 7/8) may have driver updates for your Nic in the optional section. Broadcom gigabit adapters have similar tuning parameters.
Do a search for tcp off load rss chimney, always document what setting you change, and see if that helps your Internet responsiveness.
Here is Nick Whittome, a Microsoft MVP, take on these advanced TCP tuning features of Windows
RSS / TCP Offloading strikes again. Microsoft should KILL this feature for the masses... - Nick Whittome - The Naked MVP
I'd probably try the TCP Tuning options first before updating drivers. If you do update drivers I've seen some driver updates change all the tcp tuning settings back to default a couple of times so you want to recheck your settings after a driver update. The above article - in the reader comments states what parameters to adjust. In a nutshell, it would be disabling Receive Side Scaling, TCP Offload (IPv4 and IPv6), and IP Checksum Offload (IPv4 and IPv6). The newer drivers let you make these adjustments in the advanced settings of the adapter, so you don't have to resort to manual tweaking of the Windows registry. Some adapters which don't expose these settings you may have to drop to the command prompt and issue some netsh commands.
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