Security light on?

There is no way of telling how much it will cost without following the trouble tree I posted. That code has nothing to do with the pass lock system though.I have seen that code caused by a bad battery though or someone that left there light's and ran the battery down.
B1327 - Device Power 1 Circuit Low

Schematic

CIRCUIT DESCRIPTION
Battery voltage is supplied to the OnStar Communication Interface Module (CIM) by circuit 1640. This input is internally monitory by the CIM for proper operating voltage. The minimum voltage for proper operation is 9.0 volts, if circuit 1640 drops below 9.0 volts, this DTC will fail. DTC B1327 will remain current until system voltage is above 9.5 volts for 1.2 seconds. Under 8.5 volts, communication with OnStar system using scan tool will be disabled.

DTC PARAMETERS

* Voltage on circuit 1640 is between 8.5 - 9.0 volts for 1.2 second s
* Illuminate the red OnStar LED.

DIAGNOSTIC AIDS

* Check for poor connections at the CIM and instrument panel fuse block. Inspect harness for backed out terminals, improper terminal mating, broken connector locks, improperly formed or damaged terminals and poor terminal-to-wire connections (terminal crimped over insulation).
* If fault is suspected to be intermittent, moving harness wiring may help in locating fault.

TEST

Diagnostic Chart

Thats only .25 volts that could be meter error connection error your meter leads etc. You can try checking connections wires etc that wouldnt be a bad thing. The strange part is there are no codes setting.

Try this it may help
GM PASS LOCK RELEARN- Ignition to "run" position, try to start and let key return to "run" position
Approx ten minutes security light will go off
Turn key "off" and wait 5 seconds
Repeat 2 more times for a total of 3 relearns.
Turn key off, then start it
this will let the BCM relearn the security key

Anything is possible but since you had to have it jumped to start it then I would make sure the battery cable's are clean and tight and have the battery and alternator tested and go from there. If you still had trouble with the security light coming on then I would have the body control module scanned for code's.

It sounds like the car is going into limp mode but to be sure lets run the codes to see what comes up. here is a guide to help us:

https://www.2carpros.com/articles/checking-a-service-engine-soon-or-check-engine-light-on-or-flashing

Please run down this guide and report back.