Well, either the H drive is not accessible, or it is and some files and folders are corrupted. Can't be both.
What is the make/model # of this external HDD, and has it been working properly until recently? Did you do anything that caused it to malfunction, like unplug it while still running, or drop it?
First connect it to your compute, boot into your BIOS, and make sure your boot drive, and this particular drive is recognized in the BIOS.
Then boot up to the desktop, right click on My computer, Manage, Computer Management, and in the lower left corner, click on Disk Management.
If you can, please take a screenshot of the Disk Management dialog box, and upload it (imageshack, photobucket, or other) so you can post the image with your response. That way we will be able to see exactly how your computer sees this drive, and someone will be able to give you the best advice to get your files and folders back.