You state that the "T1" is connected to 1 PC and is working ? ?
How is it connected ? ? ... Thru a Modem or right into the NIC Card ? ? ?
This is important to know so we can get you the correct information
In my experience if I use a cisco router with T1 WIC with internal DSU/CSU it will use a standard RJ45 patch cable from the d-marc, Only once did the telco wire the d-marc for frame cross-over cable.
If using an external dsu I use a v.35 (serial) cable from the adtran to router interface. The only exception was a bay router with external dsu that used an RJ45 from dmarc and converted it to v.35.
I have never heard of using linksys as a T1 router as all the external T1 DSU's Ive used are serial interfaces to router and have yet to see a linksys with a serial interface.
If you really have a T1 pipe see this link for a Router that will work with it:
http://www.dceexpress.com/Patton_Low_Cost_Router.htm