Unable To Get Most Websites To Load On My Browser?

How fun. Earlier this week, my state experienced some severe weather which ended with a tree on our street falling and the power going out all day. It took a bit longer after that for our cable services to be restored - internet included. Ever since then, my computer in particular seems to be screwing things up for everyone else. When my computer is shut off, every other computer (one laptop, two desktops) in the house has been able to connect to the internet and maintain that connection all day. However, as soon as mine connects, the connection dies within minutes - for everyone.

I thought it could be an IP conflict but every machine in the house is set to obtain their IP automatically. Interestingly enough, when the XBOX 360 is bridged through my computer it (the xbox) also maintains a connection, albeit a slower one.I have reset both the router and modem, including hard resets, and I've pinged and pinged and pinged. The same thing seems to happen regardless of whether I am using a wired or wireless connection. Here's what I have:

Computer model is HP DV6838nr.
Modem is Toshiba DAZ8821F.
Router is Linksys wrt54g v5.
I am running Windows 7 Ultimate.

I am using Firefox but have also tried Opera with the same results.

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+ Computer has been showing a successful connection in the Network and Sharing Center even when websites fail to load and the connection has gone down for others.

+ When trying to use a wired connection for the first time, the computer could not connected. IT jumped back and forth between "Identifying..." and no connection at all.

+ I reset the router with both wired and wireless connections. With the wireless, it would become functional for a few minutes after being reset and then fail again. With the wired, the router would not broadcast at all. I ended up having to unplug it for a minute and then plug it back in to get it to broadcast again.

+ I tried using my cable with just the modem, but the Data and PC lights failed to light up upon doing this.

+ After all of this, I removed the wired connection and re-enabled my wireless on the laptop. Connection was restored for a few minutes.

+ Despite a successful ping after two minutes, most websites wouldn't load.

+ Switched to a different laptop after turning mine off and was able to maintain a normal internet connection for over an hour.After starting up the computer for the first time:

C:UsersManda>ping yahoo.com

Pinging yahoo.com [67.195.160.76] with 32 bytes of data:
Request timed out.
Request timed out.
Request timed out.
Request timed out.[code].....

Interestingly enough, despite the successful pings I was still unable to get most websites to load on my browser.