What is wrong with the HD?
Does it spin up, or does it make a clicking noise?
Does BIOS see it? Does windows see it?
All recovery places will attempt a clone of the drive in question (assume it still works) and work with the cloned drive. So, if the HD still is seen in windows, that is what you should also do (assuming there isn't anything physically wrong with the HD, no funny noises, no clicking or anything like that).
For recovery services, it really depends on what needs to be done. The less the time spent on the HD in question, the cheaper it usually is, but it also depends on how fast you need the recovery done.
I have seen prices as high as $5000 for a really damaged HD that was in a fire, but, typically, the costs is around $150+.
They do have places that offer free quotes and all that as well. Both WD & Seagate have their own recovery labs in house now, so that is another option.