Transmission not shifting

Did you check the transmission fluid level? Is the condition of the fluid look red or more black/brown?
Is the check engine light on? If so, the code stored in the computer will help isolate the issue (most automotive places will scan the code for free).
Does the dealership offer a warranty with each vehicle they sale?

If the fluid level is good and there is no check engine light on, this sounds like a mechanical failure inside the transmission.

Fluid level is good and a reddish brown, more red then brown. When I put it in gear it hesitates and after I hit the throttle it will go into gear. And the whining noise I also get in park for a short time.

I would take the vehicle to a transmission shop. This is related to the transmission and revving the engine jars something loose or builds enough pressure to cause the transmission to shift/engage into gear.