I have a 2008 Mini Cooper S hardtop. How much to replace the timing belt?

If you have the R56 turbo model then you have a timing chain and not a belt. If the chain stretched and the pistons made contact with the valves then the cost of a used engine plus the installation could very well exceed the 5K mark.

I'm buying a used 2008 just under that in mileage. Frankly, your situation scares me a little. I don't have an answer, but if you can't get it here, try Quora.com Let me know how you make out.