Car accident, determining the value of a totaled car in WA state

If you want your car fixed by the responsible party you're going to have to wait until somebody takes responsibility for the crash. If it turns out that one driver was in fact responsible, that person's insurance (presuming they had some) will would be responsible for all damages caused by the collision. Unfortunately, in a multi-car collision that is the fault of one driver, there is often insufficient property damage coverage to repair all of the vehicles. In that case you have to look to either your own collision insurance or your own wallet to pay for the cost of fixing your car.
In dealing with a total loss claim, whether with your own insurance company or the other driver's, you are not obligated to accept their settlement offer. It's my experience that most insurance companies lowball their estimates of a car's total value. Arm yourself with an honest assessment of the value of your car. Look at online sources such as Kelley Blue Book, and local car sales publications such as Auto Trader and your local newspaper publications to get a better sense of the actual replacement value of your car. If you can't avoid having your car declared a total loss, at least negotiate a fair payment.
Having a higher supportable "fair market value" for your car may help you persuade the insurance company that it is not a total loss. Also, work with the repair facility to see if they can get the repair cost down to a level that brings it under the insurance companies "total loss" amount. Your insurance company might also be willing to pay for partial repairs to keep your car from being totaled. If you're willing to forgo cosmetic damage repair until the responsible party is determined, you might be able to convince your own insurance company to fix the other damage and not call your car a total loss.

Totaled means the amount of money to repair your car is greater than its present resale value. If you contest the blue book values, assemble and present evidence to your insurance company that your car has a greater value than the standard range. They will be hard to convince but it is worth a shot.