I found the answer to this. It is very apperhent that Sony mislead customers.
If you are getting the error code 8013013D it is because your PS3 does not have the ability to connect to a wireless network.Even more ironic is the fact that my PS3 will scan for and find my SSID, however because I have a 20 gb system, the Sony customer service rep advised me that it will not connect to a wireless network.
No I completely understand why Sony is bringing up the rear in gaming systems.
after another two hours we have seemed to of found a solution for all those that have tried;
everything delete home, all data for it as well then re connect your hub, we've had 4 hrs of online play without interuption hope this helps folks,
I just bought the 160g ps3 and it came with version 2.45 . EVERY TIME i try to connect to my wireless connection it says that **** error code. Some one please fix this ******* problem!
My router is a D-Link with N strength signal. (2.5)
EDIT: Hi I'm back! , I fixed my problem! No idea what it was though Anyway I fixed it by buying a 50' ethernet cable and have been getting sweet, juicy, lagg-less, multi-player ever since