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PCM - Powertrain Control Module. This does not control the a/c.
Well, first off, the battery is only available from Ford. Current prices, depending on the hybrid battery used on that model can go upwards of $2500-4000. Shop wisely.
If you have the ability to remove the transfer case from the driveline, disassemble it to get the chain out, then you should have the ability to repair/rebuild the t-case and put it back in. Good luck!
Take you car to your local Honda dealer to get the recall taken care of.
You'll need to address these issues one at a time. The Transmission is in need of a specialist to determine whats wrong with the overdrive. By running the car without the overdrive on & functioning, its costing you miles per gallon as the engine is working harder at a higher rpm. As far as your 'not running right' issue, a proper diagnostic check by a qualified technician might serve you well.
More than likely, something is blocking the ducting behind the dash or in the cowl.
Use the 'Estimator' feature on this site to direct you to pricing on these services. It will not be exact pricing, but close. You may have to use it for more than one service, if they are not done as one repair.
An accurate diagnosis by a reputable service shop that offers alignment service will be in your best interest. There is no way to tell what is causing the problem without a proper inspection of the front steering and suspension.
Look in your local phone book under 'auto salvage/recycling' and start making calls.
If your information source removed the valve cover(s) to confirm this, he/she should have given you an estimate for the repair. If 'someone' told you this 'might' be the problem, have a reputable service shop actually check the vehicle and give you an accurate diagnosis of the problem.