I have finished the schematic and the code for the project. Give them a try, if you have any problems just come back here. Lots of people in the forum can help with both. They should work for what you want to do.
I have added a few extra functions to the circuit for good measure, if you don't want to use them simply exclude them from your circuit and leave the code as is. It will work if you remove the park, reverse, or neutral relays.
The relays labeled 1 through 6 are to disable the stock shifter once the circuit is powered up. A few mistakes were made with the relay board but they should be easy to clear up. The mistakes are:
1- no fly-back diodes on any of the relays. Add one for each relay, a 1N4001 should be large enough
2- common is not connected properly to the relays, the common for the gears is from the stock shifter (yes, there should be a common in there some where, most likely a black or red wire). Common should also be connected to the common contact of relays 1-6. Relays 1-6 should be connected to relays 7-12 through the N.O. contact respectively.
3- add a diode after the power switch but before the 7805, and make C1 about 220uF or larger.
As a general note; the sensor input should be left unconnected if the park and reverse gear are not used (no reason to detect motion). Leaving this unconnected will save you some time and a bit of money but it will also allow the IC to enter sleep mode while it is not being used. If you do choose to keep the park and reverse gear, you must include the sensor to avoid damage to the car.
The first few lines of the code describe how the IC works for your reference as well as some technical information for anyone on the forum trying to help you.
In case you don't want to read through the code, I'll describe the functions here;
When the circuit is started up, there is a brief period that the IC waits while it stabilizes the internal clock (4MHZ). Once the stabilize has timed out, it loads the sets up the hardware to be used. The IC will automatically start with the neutral gear selected, this eliminates the need to test whether the vehicle is moveing on start up. This is also something to keep in mind if you are trying to climb a steep hill. It then scans the inputs for any gear changes. It will scan a few times then check whether it can go to sleep (by checking for spinning wheels). If the vehicle is still moving then it will stay awake and continue scanning. If you stop in traffic then it will go to sleep and wake up again once you start moving.
To change gears, hold the button that corresponds to the direction you want to shift. You must hold if for a minimum of 260ms (0.26 seconds) before it will shift up or down. If you hold it longer then it will shift into one of the other modes based on the held button. If you hold the up button for more than a second, then it will shift into neutral. Hold the down button it will check to see if you are moving, if not (or very slowly) it will shift into reverse. Holding up and down at the same time will shift into park (if you are not moving). While you are in any of these gears and you press up, it will automatically go into drive. If you press down, it will automatically go into first.
Any questions?