Well, here is my personal take on your situation. Your ADSL modem works just fine, the problem doesn't lie with that, it lies with your PS3. If it is giving is a LAN error then you can try the following things.
Check the IP adress of your laptop and your PS3, there may be a conflict.
Check your PS3 for any special wireless settings, there may be a certain method to get it to work with the PS3 unit.
Your scanning for wireless networks with your ps3 and finding the router, however if it is coming up with an error then it isn't connecting to the router. i would personally check into your router and see if it is excepting the IP adress that is given to your PS3 unit, perhaps your router isn't set to except the IP range in which your PS3 is in.
if all else fails, i would see if there is a standard wired port on the back of your PS3 (unfortunatly i have not seen one in my life, so i can't tell you) and connect it... if at that point you still have an error then check your IP settings.
Sometimes with DSL/cable modems at least for windows you need to set your IP adress to "obtain IP adress" instead of a set adress.
other then that, i would check into sony's website for trouble shooting that problem, or even call then tech support line for more information as to how you can get this problem fixed.
i hope the info i gave you helps, if not then i'm sorry i couldn't fix the problem... unfortunatly i never dealt with a ps3.