Laptop wont stay connected to internet...is it laptop or router?

OK, so here is the deal: about 6 months ago I purchased a brand new laptop and connected it to my DLink router that has been working on our PC for about 3 years now. I also have 2 Playstations and 2 other laptops connected to the D Link (all of which are working fine and NEVER have any problems whatsoever). About 3 weeks ago, I turned my laptop on and tried going online, but much to my surprise, it couldnt connect. Its supposed to automatically connect, but this time it didnt. I figured I would manually connect it. I opened up the window that displays all the routers that the laptop is picking up and i saw my D Link so I try to connect. It attempts, then says "connected" and the after 3 seconds or so, it says "Limited Access". I thought it was a problem with the internet so I checked the other laptops in the house and the Playstation and they are all working fine. I figured it was my laptop so I shut it off and restarted it but it did not work. Next, I tried unplugging the router and waited for 2 minutes or so and plugged it back in. Yay! It worked! I solved the problem! I began surfing the internet for a couple hours when, BAM! It suddenly went out again. I figured I would unplug the router once again to see if it was just some kind of glitch and would work fine this time. I unplug it and repeat the process over again. after 2 hours, it goes out. Everything else in this house seems to be working just fine on the router with no problems whatsoever, except mine. I have not messed with any of the configurations because I have not idea where to even begin so I know it cant be with the configurations. My laptop is new with windows 7, I'm using xfinity as a provider.

Side note- I did a test and when I cant connect to the internet with my laptop it fails a "PING" test (no idea what that is), but when I unplug and plug up the router and the internet is fine on the laptop, it will pass the "PING" test.

I'm completely clueless about all this, I really hope someone can help. If you have any questions, any at all that might help you diagnose the problem, please ask and I'll try to answer as quickly as possible, I really need this problem fixed. Its horrible having to reset the router every 2 to 4 hours.

Recap: New laptop with windows 7, all other laptops and PS3's work just fine even when MY laptop isnt, fails "PING" test when it cant connect to internet, passes "PING" test when it can connect to internet, unplugging the router and plugging it back in will give me internet for a few hours, when laptop cant connect it says "LIMITED ACCESS".

any ideas? Thanks to all who help.

P.S. Like I have mentioned before, I'm a complete newb and dont really understand too much of the lingo, please break it down barney style for me. Thanks again.

From a command prompt do (ipconfig /all) when it works and when doesn't. Also take one from a working PC when the new PC stops working.
Attach them to your next post this will help to trouble shoot your problem.