Don't worry about checking grounds just yet, these are your what are causing your starting issues, the next time it happens I'd be willing to bet that your "security" light will be flashing.

Most likely the pellet on the key is dirty or the contacts inside of the ignition switch that complete the circuit to read the resistance of the pellet are dirty, swab the inside rim of the ignition cylinder with some isopropyl alcohol and clean the pellet with that also.

 

The P1631 is probably the result of an "incorrect" key being inserted in the ignition.

The B2723 is also set when an "incorrect" key is inserted in the lock.

So what is meant by an "incorrect" key ??? The B2723 is set when the BCM tests the reistance of the pellet in the key, and the detected resistance does not match the expected resistance programmed in the BCM.

When this condition occurs, the BCM does several things ...

1) stores the B2723 code
2) Sends a message to the IPC to illuminate the SECURITY lamp
3) disables the Theft Deterrent Relay
4) stops the PCM from delivering fuel (which sets the P1631)
5) Sampling of the pellet is disabled for 3 minutes
6) The steering column remains locked (depends on column lock recall, of course)

Note that number 5 is important, even if you immediately re-insert the key, and it would have "passed" the test, it doesn't matter, for 3 minutes the BCM will not sample the key. ALSO - IMPORTANT - if you insert a key in the ignition during this 3 minute "timeout", the timer re-sets and starts again at 3 minutes. Disconnecting the battery will also do the same, re-start the timer at 3 minutes when the battery is reconnected.

Clean the pellet, and the ignition lock as well as you can. If you have one of those 10 pound key rings ... get rid of it, the ignition key should have nothing more than the fob attached to it. Heavy key rings tend to wear the lock cylinder and lock mechanism more quickly, and can contribute to a false reading of the pellet as the weight of the key reing can cause a poor connection in the pellet reader area.

 

Mine did this when I first bought it. Turns out the battery terminals were not tight. With a little effort I was able to rotate the connectors. Tightened them up and had no problems since. Cured my headlight fade everytime I applied the brakes also.

Bill

 

I've replaced the battery and the battery terminals but I think Stephen has hit the nail on the head. (the Theft Deterent System)

When I inserted the key the BCM test failed.
Of course I would continue to turn the key to try and start the car but all this did was reset the 3 minute counter. The 3 min disable feature explains why I was fooled into thinking I resolved the problem, several times.

First time it failed I jumpered the clutch interlock. Tried it again and it worked but the problem was not the interlock, instead, the 3 min disable had expired and when I tried it again it worked. Fooled me into thinking I had solved the problem.

Second time I relaced the battery. Same result.

Third time I replaced the starter. Same result.

Now that I know more about the TDS I'm taking a more thoughful approach instead of just replacing parts.

#1 - Cleaned the key and VATS pellet
Also I plan to clean the ignition cylinder (how?) contact cleaner?

Thanks for all the great advise. (I love this Forum
I've learned more on this Forum than I ever did by reasearching the manuals ... Forum members help you get right to the meat of the problem (quickly). When I first started having this problem I should have posted a question. A quick post may have saved me the cost of a new battery and starter and my labor :o