2001 Ininiti Stereo system gets stuck

I have bought 2001 Infiniti I30 recently and I saw that I cannot skip tracks in cd, switch to Tape, switch to radio when I start the car. After the car is driven for 25-30 min, it starts working properly. It also has a CD changer installed in the trunk. The only button that works on the system in the first 30 min is switching between 6-cd changer and the in-dash CD player.

Now I found out accidentally that if I press CD/CHG and TAPE at the same time then I could switch to TAPE, even in the first 30 min.

I do not know what's happening exactly. Is it a common problem? How m uch would it cost to do a repair on this?

My wife also observed that sometimes the stereo sturns on by itself and goes off. Even the switch between the indash CD player and the 6-CD changes happens randomly. This didn't happen that often yet.

We bought the car just last week. Let me know if anyone has any idea regarding this?

Thanks

Karma