How do I claim the diminished value due to the other car's fault

You probably can't do it.  I understand about the diminished value of your car, but the law isn't perfect.  The cost of repair is all you are usually entitled to get.  Part of the problem is that what your loss is, for the diminished value, depends in part on how much longer you keep the car.  If your car is worth, for example, $7,000 today instead of $10,000 because of the accident, a $3,000 difference, if you keep the car for another two years the difference might be $3,000 instead of $4,000, only a $1,000 difference. And yes, I know it's likely you'll have more trouble with the car during those two years, but the law doesn't usually look at losses that are speculative like that.

If you want to get a firm opinion on this, you should talk to a Kentucky attorney.  One place you can find a lawyer is our website, http://attorneypages.com

When you make a claim with the at-fault driver's auto insurance company, they will want you to get an estimate for repairs to the vehicle.  The insurance company's duty is to "make you whole" again, meaning, get you back to where you were before the accident.  If your vehicle has some special value because it is a classic or has some specialized paint job or equipment, you will need to document that in writing or with photos to the insurance company.  If, indeed, the value is diminished even after the vehicle is repaired, and you can prove it, you should be compensated.  If the car was a total loss, be sure to provide proof of the value of the vehicle with whatever special extras that make it so, to the insurance company when negotiating a settlement.