Ok, i've had this problem, i feel like it's my job to help you out now, the download limit means nothing about how long you can play, it just means how much you can download from the internet, so lets say movies, if you download over 3GB of files, then you went over the limit, so remember, it has NOTHING to do with how LONG you play online with the internet.
Ok, next step, i ain't to sure about the modem, as i use a set top box (PACE), but when people were talking about the modem, all you need to do, is pull the plug out of the modem, wait about 2 min's at most, to make sure, then plug it back in. Then put the CAT5 cable, from the modem, into the PS2 network adatper, and thats it, then do the same thing as before, to go back onto the PC/Laptop, so it's best if you get a router, which i just got about 2 days ago, so if you need help with a cheap router, just ask.
Depends how much you play on the PS2/laptop/PC, if it's like 3 hours a day, then there is no need, if you got a brother/sister who wants online, then you may want a router, just like myself, we take it in turns to go on the net, so it was best to get a router.