Any data recovery will ask if the drive has been opened and they won't like that it was. Not saying they won't take it. They just don't like it and could say no.
Here is some text from a data recovery center website.
"The collection and analysis of a failed hard drive costs data recovery services a significant amount of money, there has therefore to be some kind of possibility that the data on the failed drive will prove to be recoverable. While we do charge an analysis fee it does not cover these costs and so we have to reserve the right to charge more if the drive has been opened previously. This doesn’t apply where the drive has been opened by other recognised data recovery services as they will have done so within a clean-room environment. Many data recovery services will simply refuse to accept hard drives which have already been opened.
Once you have opened your drive out-with a clean room environment you have exposed the drive to the risk that contamination (such as dust particles) will become stuck to the platter surface. When the drive is subsequently powered-up the dust particles become lodged between the read /write heads and the platters surface. During normal operation these heads should never make physical contact with the platter surface, they float on a minutely thin layer of air just above the surface. These platters are typically spinning at 7200 RPM, you can imagine the devastation to the platter surface should a dust particle become wedged between the head and the platter surface, it will literally grind your data off that platter surface in a fraction of a second.
People who will open a hard drive out-with a clean room environment are not likely to take the other necessary precautions required during the analysis of a hard drive, such as anti-static handling procedures for example. The number of previously opened drives that we see here with fingerprints on the platters clearly testifies to the widespread lack of care taken when drives are opened by amateurs.
For all of these reasons most data recovery services are reluctant to accept hard drives which have been opened at home by the end user of the drive."