External Hard Drive Recognized, Not Working

Hello,

So, I have recently run into a problem with my Seagate FreeAgent Go Flex 500gb external hard drive.
Since about November, it has worked perfectly fine. No errors, but it was a bit slow with transfers and some times slowed down my computer. I don't know if those were supposed to be a sign of what was to come, but I thought I'd mention it.
Just earlier today, it asked me if I would like to format my drive.
Now, I had only ejected it improperly two times before hand, but those were both accidents and they were close to the time I first recieved it. I didn't have time to eject it before it fell off of my desk. It hit carpet, not hardwood or tile.
Now, it isn't making much noise, but the power adapter is working just fine. It's warming up, and it's a USB 2.0 that is capable of USB 3.0 with a driver that is on the EHD. I've tried every possible way, except for chkdsk because I honestly don't know a safe, non-:/C harming way that might actually work.
My computer recognizes that it's in the port, as does every single other program that deals with disk drives. It's powering up, obvious by the warming up, and there are no odd clicking or beeping. I am 100% befuddled by this problem, and I need EVERYTHING that is on this drive.

Do I really have to re-format this crucial drive and re-obtain most of my files? I have no back-up of anything on this drive, and I will definitely make one if I can fix this.

Please, I need this hard drive really badly.

Answers, please.