|Well, first off you should have made backups of the data.|
That said, you have two options. First one is professional data recovery (very expensive). The second one is to remove the hard drive from inside the enclosure and try connecting it internally.
If the hard drive does not spin up then the bearing may have seized up or it is possible the PCB is fried.
One method that sometimes works if the bearings are bad is to chill the drive down by placing it tightly in a plastic bag in the freezer. After removing it you MAY get it to spin for some time.
If trying this you need to plan ahead. Where to copy data and what is most important. When the drive warms it may quit spinning. If you have crashed heads and you continue to play with the drive you may end up damaging the platters. That would mean that even professional recovery may not work.
Only you can decide how important the data is.
Go to the website of the manufacturer of the drive if it was sold as an external complete unit. There may be help there along with diagnostic tools and possible recovery services.
See link below.