Frustrating and bizarre dropped connection

Hello Everyone:

I appreciate you staying with me as I am not a computer expert by any means (not quite a newbie either). I have been experiencing an interesting internet connection issue for quite awhile now (3+ years) and it appears to be getting worse. I am currently running Windows 7 x64 on an HP desktop machine. I was previously running Vista x64 on the same machine. Here are the details:

If my computer has been on for a fair length of time 8-10 hours (but now dropping to 3-4hours) my internet connection will drop but here are the interesting points. My connection drops whether I'm wired or wireless (currently using a Linksys WRT54G) and I have tried plugging directly into the Motorola router I have through Time Warner with no relief. If I am streaming a video or having a chat conversation in say, Google chat, I can continue doing that but I cannot access any new web pages and I get the no connection screen on my browsers. I have tried this in Firefox, Chrome (my normal browser) and IE. Meanwhile when my connection drops I am still able to access the net on my tablet or droid phone. A quick reboot of the system brings the net connection back immediately every time. Resetting the routers also brings no relief to the issue.

I have updated all of my drivers countless times and tried a few other settings to no avail. I would greatly appreciate any advice that anyone on here can offer. Thanks again.

Have you tried doing a factory reset on the router and reconfiguring it again? Do you have any device in between the router or something? Have you done a Tracert on some internet site to see if there is a lag at some hop? They only thing you can do to prove that you dont have an issues is replace what you can, either NIC, cables and try a different slot on the Mobo.

I am running a Linksys wireless router into the Motorola modem that Time Warner provided. This is not the first Motorola modem I have tried. I have reset the Linksys many times. I have not done a Tracert as I am unfamiliar with what that is. I haven't messed with it to any great extent as it has just been an inconvenience to this point. Hardware replacement is something that I will obviously consider if this gets any worse.