I am assuming that your broadband connection is to a USB adsl modem attached to your present pc.
The easiest way to do this would be to set up an ad-hoc ethernet connection between the 2 pcs. This will require a PCI ethernet card in your ME computer and a CROSS-OVER ethernet cable long enough to connect the two pcs. You can obtain these very cheaply either from a local store or the eBuyer web site: card £4 click here cable £2.65 for 10 metres click here
Basically, you install the card in the ME pc, connect the cable between the 2 pcs and run the Networking Wizard on the pc attached to the internet; follow the instructions in the wizard.