need help networking a new computer

okay so heres the deal, i have a new pc that im going to set right next to my other one. i have wireless internet, on my current one, and its unfortunately propriatary from bellsouth and i dont feel like spending over $100 for a stupid card/usb adapter. i have plenty of cat5 cable, is there a way to physically wire my newer pc to my network through my old pc without having to run line all the way from the modem/router...pretty much the old school way. and if so how.

 

Your request sound reasonable if a “Stupid” Card would cost $100.

Since a smart Card can be found for $20, it does not make sense to solve it in a different way.

Any other way would need double Routing.