Firstly you need to narrow it down to 1/. Computer or 2/. Internet, i.e. does this only happen to gaming online or does it happen offline, the comments on the modem may be valid and you may want to check firmware/software.
If computer the mostly likely culprits are the ram or the video card, if you can swap these out then fine, if not then it becomes a lot more difficult, if online then try turning off background programmes one by one. I had this years ago when the ram on my bang up to date video card was incompatible with the motherboard, fixed by a (very dangerous in those days) motherboard flash.
