Hi

I think Gupsterg has answers for battery and coding. When you do replace the battery after disconnecting the power the steering sensor needs to be reset, just turn the steering lock to lock a few times.

Blowing hot air sometimes could be heating control valves. It is easy to try cleaning which worked on mine.

Here some help from another site.

Here’s what to do…

Caution: Do this only when the engine is cold so there's no pressure in the cooling system.

Fig 1: Remove the plastic cover between the back of the engine and the firewall (not shown) by lifting the spline from the front edge and gently pulling the cover towards you. With that removed you’ll be able to see the location of the pump valve unit (yellow arrow). One plug and those two little cans are all that have to be removed.
http://home.ptd.net/~rstoer/images/1location.jpg


Fig 2: First remove the rear plug* by placing a small screwdriver where indicated by the green arrow. With the front of the blade under the plastic edge, gently press down. When you hear it click the plug will slide right off. The red arrows on my photo don’t show up too well but you can see the three #10 Torx screws across the front edge. There’s three more across the back. Remove the six screws.

* Update: Someone contacted me to say that he successfully used this method, except he left the coil assembly in the car because he had trouble removing the plug. It's true, the items that require cleaning can be accessed by just removing the six Torx screws. The coil assembly (the yellow and brown item in fig's 4 & 7) can be left in the car, tethered by the wires. Just make sure those two bronze washers (one inside each coil) are accounted for before allowing it to dangle about in the car.http://home.ptd.net/~rstoer/images/2removal.jpg


Fig 3: With the plug and screws removed, lift the two cans and the socket for the plug you just removed as one unit. Wiggle gently if needed, but it should lift off pretty easily. Be careful as one or both of the plungers may come up with the housing, making the plunger springs vulnerable to falling off. The photo shows one plunger & spring still in place.
http://home.ptd.net/~rstoer/images/3valvebase.jpg


Fig 4: This shows all the parts you’ve disassembled. (I took this photo after cleaning everything).
http://home.ptd.net/~rstoer/images/4parts.jpg


Fig 5: This photo shows the solenoid plungers, springs and washers. Note the caked-on substance on the un-cleaned plunger. I found areas of this on both plungers and the brass sleeves the plungers fit in. It’s what causes the sticking, and a good cleaning of these surfaces is all that’s needed to effect a cure. Just make sure you get it all off. I used Meguiar’s Mirror Glaze fine-Cut Cleaner because that’s what I had. Anything similar would work.
http://home.ptd.net/~rstoer/images/5plungers.jpg


Fig 6: On the housing I used a jeweler's screwdriver to gently scrape off most of the sludge, and the Fine-Cut Cleaner on a Q-Tip to get the rest.
http://home.ptd.net/~rstoer/images/6housing.jpg


Fig 7: Here’s everything cleaned up and ready to be reinstalled. When you reach this point, place the coil assembly right-side up (mine's shown upside-down), and insert a washer into each hole. Then place a solenoid housing over each coil. Finally, slip a spring onto each plunger. The nine parts should now comprise three sub-assemblies.
http://home.ptd.net/~rstoer/images/4parts.jpg


Fig 8: I found no crud on my valve base but check it and clean as necessary. Insert the plunger/spring assemblies into the valve base (only one is shown in place here). Press each one down and see that it pushes all the way in and springs back freely. Then fit the coil assembly over the plungers, making sure it seats properly on the base. Reinstall the six Torx screws and tighten. Snap the plug back into place on the coil assembly and you're ready to test.
http://home.ptd.net/~rstoer/images/8valvebase.jpg

The ABS stored faults you have I had on my car when I had some problems. There was nothing wrong with ABS. Sort the battery etc. clear faults with VCDS and see it any other faults come up after driving for a while.

In a bit of a hurry to go out but hope this helps.