Can a failing pcm cause Trans problems

Do you mean the 4L80-E trans? That is the one that came with the vehicle.

Regardless, the transmission shifts are controlled either by the PCM, TCM, or VCM. Now the question is this, does it slip or does it have a delayed shift? If there is a slip (no torque) when it shifts into 2nd gear, to me it sounds like it could be a pressure sensor (allowing trans pressure to drop low) or it could be an internal issue such as a worn intermediate sprag, excessive eccentricity, or the sprag is rolled over or damaged. The only way to check theses items is to remove and take the trans apart. As far as an electrical issue regarding the PCM, one of the other control modules, it should set a trans code. Also, usually the trans doesn't experience a slip, but rather failure.

I would start with checking pressure to make sure it isn't low allowing the clutch pack to slip into gear. If that checks good, I feel it may be an internal issue.

No it does have a 4l60e. That is what my fear was, I never have had so much trouble with any company with a warranty. It looks like I need to bring home my trans pressure gauge and take down the pressures. It slips it revs about 300 to 500 before it engages 2nd gear. The confusing part is no check engine light. And when I had this problem with the last trans it had about 20 on it. There warranty rep keeper telling me that it was a pcm problem. But I had to prove them wrong with the line pressure test and a video of the tach showing it was slipping.

Check the pressure and let me know what you find. It could be a simple sensor issue. If the sensor is working at all (sending wrong info) it may not send a code.

I have to be honest, I did some checking before I replied to you. Everything indicates a different trans for this vehicle. Was this something that you changed or was recommended to you? A different trans may be causing issues with the PCM or TCM. Just a thought.