Carriers will almost always say that it is the customer equipment as a cop out.
Have them loop up their smartjack. If that is successful, have them send you a loop to your router.
When they say that they have you looped,
type: show int interface
Where interface is your serial port, such as s1/0.
If you see anything other than "loopback not set" under the interface, then you are likely seeing their loop and it should work fine.
Another thing that you can do is to send them a loopback and see if they see it.
Go in to config terminal mode
Go in to the interface
Type: loop line
Then ask them if they can see your loop. If they do, then all is well. If they don't, then it could STILL be them.
Next thing that you can do is to take an RJ45 wall jack (female. the one that you punch the individual wires on), and cross connect with 2 pieces of shielded wire, pins 2 and 5 and pins 1 and 4. Then plug that in to the T1 cable.
If they can't see that, then it is either them or the cable. If you want to rule out the cable, plug a straight through Ethernet patch cable in to the connector that you made, and plug that directly in to their smartjack (removing the T1 cable that goes to your router).
If they can't see that, then it is definately their equipment. If they see those, and still don't see your router, plug the cable and connector in to your WIC port and see if the router sees the loop. If it doesn't, then it is toast.
Generally it would be the module, not the router itself. If you want to rule that out, move the module to the other slot, configure it up, and see what happens.