2001 VW GTI starting ptoblems and shifting problems

daughters car and very hard to start. Cranks but won’t fire until after many attempts. new battery and new plugs. Old plugs were well used and clean. Runs well after starting. Automatic trans and for some reason will not shift into highest gear, stays in 3rd. Asked daughter if she noticed high rpm while on the highway, YES. Is this electrical as in computer or mechanical as in linkage. or just lots of $$$$. thanks the Dad.

Has anyone checked to see if there are any error codes stored in the car’s computer. Many auto part stores will read the codes for you for free. That might help a lot with both problems. Has the CEL come on while driving? Does it come on when you first turn the key to on?