Ive been trying to get PSN to work but i cant. I originally hooked my cable to the router and it gave me a message saying, "an ethernet cable is not connected". I thought it might be my cable so i went out and bought another one but the message didn't stop appearing. Then i tried a differnt router but it still continued to happen. Ive been trying to figure this out for hours but it's no use. Any help would be appreciated.

I forgot to mention that when the ethernet cable is connected the  message saying "an ethernet cable is not connected" constantly blinks. The router slot aswell keeps blinking instead of just staying still.
 

 
Have u tried setting up your network connections manually on the ps3?
 
Best,
 
3Ball

 
Yes, I would get failed connections but when it started to say successful it said i had to update my system but when i tried it wouldn't and i started to get failed connections again.

That sounds like a busted pin.  Take a close look at the ethernet port on your PS3 and see if one of those 8 pins is missing, bent, or broken.  If so, call support and see if you can get them to fix/replace it.

 
I just checked and there all perfect.

have you tried plugging a computer or laptop into the same cable/port on the router?

yes

And was the computer able to browse the internet on that connection and did it obtain an IP address from the router?
 
If so, I'd call Sony's tech support because you have just proven that the cable and router are definitely working in the current configuration.
 
If not, then I'd say it's pretty obvious what direction to start troubleshooting.