DSL and Cable modems usually only like one PC. They identify it by the MAC address of the NIC. The way you usually get around this is with a DSL/Cable router which offers the DSL Modem a single MAC and still allows connection of from 4 to 8 PCs to its switch side. CompUSA usually has one on sale for $20 to $40. The Wireless 802.11B models are being phased out for the faster 802.11G's but are fine for DSL and usually come with 4 LAN ports.
The procedure to get the modem to recognize a new PC varies. Sometimes you can just press the reset button on the modem. Other times you have to power it off and disconnect it from the DSL line then power it up and then power up your PC then connect the line. Ask your DSL supplier or check their website.
It is odd that you don't get a link light to stay. Usually they just won't give you an IP address or let you pass through to the Internet but perhaps your modem is a bit more unforgiving than most.
Both the MAC and the PC use the same cable so if it works for one it should work for the other.
Ron