HI ALL

I've purchased a used 1999 S-500 in excelent condition with 110,000 for $3,500 i did now the check engine light so went i was test driving it i took to an auto zone and there was two codes for bank 1 and bank 2 so I dcided to buy car after a long test drive and knowing the cause of the check engine light. I took the car for a drive today and we went through a mountain ride so the were a lot of hills and put the car on 3rd gear now its stuck in the 3rd gear it changes perfectly from 1gear to 2 and 3 no slipping or nothing it just doesnt change to 4 or 5 gear any thoughts im gonna rescan the car tommorow to see if any transmision code pop up but does anybody had this kind of problem before??

 

Update!!!!
THe car is Shifting well now into all gears someone told how to reset the transmision comp. and is shifting properly. Now when I purchased the car on friday it has three codes now have 4

P0410=SecondaryAir injection system fault
p0432=Catalyst Efficiency low bank2
p0422=Catalyst Efficiency low-bank1
p0715=its a trans code and is related to input speed sensor( this is the new one that appear)

any thoughts ideassss????????????