The first thing you should be worried about is the integrity of the drive. Get an external HDD enclosure and make sure the entire drive still works. If the actual port fell off, it may be possible to reconnect the port, but the odds are against it if it's as bad as you say. In any event, as long as the drive itself is fine, you can just get an enclosure and use that, but it will probably be more unwieldy than the original case.

If the data is important and the fall was from a significant height (3 feet or more), you should get a second drive and copy your files to it as soon as possible. It's possible that the drive has some kind of internal measures to minimize damage and that the external drives are built to be more durable than the OEM internal drives that are never meant to move around much anyway, but you can't be too careful. I lost two externals to this mindset, but maybe I'm just not so lucky. I would first try to realign the connector and see if it can be snapped back into position, but if you don't trust the case anymore, nothing's stopping you from simply getting an enclosure and using that from now on. I would check local stores first just to save on shipping, but Newegg is always a good choice too.

I recommend a HDD-to-USB cable set like this one. It's unwieldy compared to the dock, but it connects SATA and IDE drives just in case. It's best suited for temporary connections, so everyone who does any work in computer repair (for fun or profit) should have a set.

Does it still work in the old case? If not, since no partitions are showing up, the most common cause in my experience is that the master boot record is damaged. I can't explain the finer points of hard drive structure here, but without a working MBR, you won't be able to do anything with your drive, even if you don't boot from it. Read more here if you're so inclined. Luckily, if this is the case, there's a duplicate MBR on your drive that can in most cases be copied to the broken one. If this is the case, copying it will instantly restore your partitions. The above link explains that you can use FIXMBR within the recovery console with the Windows CD or, since you're using Windows 7, the same tool in the Repair Your Computer option in the boot menu to repair the MBR. I would not do this unless I was absolutely sure the MBR needs fixing, which you can't check with FIXMBR. As written in the link above, the only way to do that is to look at your hard drive with a hex viewer, which I don't think the recovery console has.

When the recovery console doesn't do it, I've always used Active@ Partition Recovery to restore it. It costs $40, but it's worth every last cent as it has worked in the worst of times for me. (In the past, I've used the DOS version of Partition Table Doctor for MBR and boot sector recovery, but they don't sell it anymore.) Download the demo and see if you have the option to restore the MBR. You won't be able to copy the backup to the original if neither one is valid. In this case, you will have the option to write a generic MBR to the drive, which should be fine if it wasn't formatted in a special way (e.g. RAID). Whatever you do, make a backup (dump) of the MBR and the partition table first in case something goes wrong.

If you can't or don't have to restore your MBR, see if scanning for partitions reveals files you need. This will probably not work since you have no visible partitions whatsoever at this point, but if you can do it with the demo it's worth a try. Most likely, you will see a bunch of partitions that you never remember creating and look eerliy similar to each other; this is normal. Only one of them will be the one you want, which will be rated by Partition Recovery as a best match. Normally, you'll need to delete partitions to restore the one you're looking for, but again, since you aren't seeing any, this isn't a problem at this point. And you can always restore your partition table backup if you need to. But since you're being asked to format the drive by Windows, I would recommend holding off on this until the MBR is confirmed to be working. If it is working before you try this, then it could be that the partition table needs fixing. Let me see the result of a QuickScan before you try recovering.

Finally, if at all possible, get a drive bigger than the one you're recovering (1.5TB in this case should do it) and dump a disk image to it before doing anything else. It will take an eternity with a 1TB, but doing it will give you absolute safety however you choose to operate, so ask yourself if the data is really that important. I'm guessing it is. And if everything does turn out alright, you can always return or sell the drive in the end.

Also, since your disk is in disrepair, never do any other operations on it, defragging and formatting especially, until it's fixed. Don't even try something like that after it's fixed, because next you'll need to copy all of the files out to another drive and get a new one to replace the one you're recovering.

Hang on. Is the scan still going? If so, save the results when it finishes, then unmount the drive and plug it back in.

If it really takes that long for a QuickScan, you may as well go on vacation after you start a SuperScan if you have to.

I'm saying that you should try to remount the drive after the scan finishes because there's a chance that Windows hasn't read the new boot sector yet. It's been a long time since I had to do this, so I apologize for not mentioning that first.