I accidently dropped my external HDD. I have no clue what wrong w/ it. My hypothesis is the driver is dead. The only thing that I'm not sure is, you still recovery the data from it? Also if I mail my HDD to the company, how much will it cost and will they recovery ALL of my data? My external HDD: Seagate GoFlex FreeAgent Desk External Drive.
Your options are to take the drive out of the enclosure and test it in another enclosure to rule out the enclosure being the issue. You could take it to a local repair place if you didn't want to bother with that yourself, and they may even do that for free if they aren't able to recover any data.
If that option doesn't help then sending it to a data recovery center as you mentioned is probably the next step. The cost ranges greatly, but probably starts around $600 and goes up to $2,000 or so depending on how damaged the drive is.