I had a similar issue with a Toshiba IP PBX that I was told I had to buy expensive card to make it work with my CME or Asterisk box. I just create a couple of sip extension on the Toshiba PBX and had my asterisk box connect to those extension. Create call route for calls to be routed using those connection when calling extension numbers on my Toshiba. You will need to educate yourself about that InterTel PBX. Once you know how to create a SIP entension or a SIP trunk you are set. Create the SIP truck, then create the cal route.
No need to mess with T1 or PRI connectors. There a PRI technology called QSig you can use to connect 2 devices suing T1 technology, but I would not recommend it. Stick with IP (SIP or H323).
Good luck.