I bought a PS3 (Slim) yesterday.  I installed and connected it to DSL Modem and a router.  When I turn the game on, it immediately disconnects/interrupts my internet service.  I have 2 computers on the network and have reset the DSL Modem and Routers by unplugging and plugging back in (as suggested by PS3  Tech. support) Also, the other  computer receives a  pop-up message that 'another system with the same IP address is trying to connect, etc....". 
Does anyone here have any suggestion as to how to correct this issue with the disconnection  of internet as soon as I power on the PS3?  Thanks in advance.

You may be using the same IP address as the computers, that happened to me when I used my DS online.  Try adding an extra number to the last digit of the IP address you are using and that should help.

Are you setting a static IP on your computers? If DHCP is enabled on your router, it doesn't seem like this should be happening.

Its something wrong with your router assuming that you have your ps3 setup to find a ip and such automatically, If this is the case then the router is giving it an ip address that is used by another device.
Your best bet is to find an IP address not being used *via your routers setup pages* and set the ps3 to use that ip instead of automatic.

" @Br3adfan: how do I do that? Im a noob at this? "

What exactly is a "Media Server" anyway?

Br3adfan is the winner. I had this exact problem and I do believe that is what fixed it. Go forth!

" Try turning the media server off on the PS3. Good luck sir. "

"What exactly is a "Media Server" anyway? "

thanks so much everyone for your help and suggestions.  I will give your solutions a shot.  I knew I came to the right place.  Calling Tech Support at PS3 was a waste of time.  It's all automated.  At least here I get real help from real people.  Or are you, hmmmm. jk, lol.