1996 Audi A6 (c4) 2.8L 12V, V6, Base, FWD, AUTO, 121,000 odo

Parts replacement History:
Water pump, timing belt, routine maintance (sparkplugs, wire, ects), Radio, belt, light bulbs (head lights, tail lights, and instrament panel) and Tires

I have 2 problems that may not be related to each other.
They are the Check Engine light and the Airbag light.

Airbag light:

A couple weeks ago my car died infront of Quicktrip. I could not get it started. I suspected a dead battery but could not determine if it was the battery or the started was broken.I tried to jump it off the Front Battery Port in the engine bay but it would not start.

I had jumped other cars from the Front Battery Port a week earlier and it worked fine (The batter is under the rear seats).

I had it towed 4 blocks back to my house and decided to try to jump it again before replacing the starter the next morning. This time I connected it directly to the battery instead and it started just fine. At this point I had no other issues that a dead battery (it was from 2002 and it's 2010). I replaced the battery and noticed that the airbag light stays on for roughly ten mins and then goes out.

My concerns are: does it work after ten mins? why would changing a battery cause this? I have unpluged the battery to replace the radio twice and also connecting a aftermarket amp but didn't have this problem before.

Check Engine Light:
Yesterday I replaced lights in the instrament panel. I have done this before so I was familier with the process. I took off all the pieces to get the instrament panel out. I unplug only one set of wires so I can get it out just enough to replace the bulbs. I replaced the bulbs and tested to make sure they were working. Thats when I noticed the Check Engine light was staying on. I put everything back together and drove around the block. Everything seemed fine. I drove a couple other places later (at longer distance and time) and I could not tell a difference in the cars behavior except now I have another light on.

Both lights are on the right side when the cars starts and does the start up checks. The center indicator screen starts up normal and shows ok and goes blank like normal.

I need a a emissions and safety inspection done in or before Decemeber and I'm guessing it will not pass unless I fix these problems.

I'm grateful for any help or suggestions. I can provide more pics and info if needed.