My computer does not recognize my 1.5tb hard drive. which means I cannot open it to recover my data.

Try other usb port, or other computer and see whether the hdd is detected. If still not, try to go to device manager ( http://www.computerhope.com/issues/ch000833.htm ), and then assign a drive letter to the hdd. After that, try to access it from Computer, if not able to access it, format it (use quick format) and then use this program to recover your files.
http://www.asoftech.com/adr/

Kernel for FAT and NTFS is the software what you need in this case. It can effectively recover data from corrupt or formatted hard disks.You can get the software from following address.
http://www.windowsdatarecovery.com/

From your description it appears that your 1.5TB drive is failing. You can try to check if there are problems with the drive using the free trial version of http://www.hdtune.com/

If it checks out ok then you can try to recover your data with Recuva it's free http://www.piriform.com/recuva

Or if you need data recovery help this a good choice for low cost and fast data recovery. All data recovery work is performed by an experienced tech remotely over the Internet from a boot cd that you download and the best part is they just ask for donations: http://FreeDataRecovery.us