I recently bought a 250GB hard drive from ebay and it also come with a transfer cable
MY intention was to upgrade from 60 gb to 250.

So I got the cable and after some difficulty on trying to find a program that will allow me to copy over partition 3. Xport. Now for some reason when i plug in the 250gb hard drive to the cable the computer wont recognize it. I dont remember even trying to check before. But all I hear is some weird clicking noise. However, when I put in my 60GB my computer recognizes that something is plugged in, you hear that sound.
/
So you would think that maybe my harddrive is broken?

I put it in my 360 and it is recognized as having 229GB (im assuming the rest is for system data)
I can save data to it and all that. Like its a regular haddrive.

I plugged it back into the computer..still isn't recognized. I even formated it on the xbox 360, and try to plug it back into the PC still doesn't work.

I dont get it, why does my 60gb get recognized by my 250 wont

How do you connect it on your PC? Please be as precise as possible.

I plug it using the USB tranfer cable that came with the purchase. THe 250 harddrive goes into adapter which goes into the laptop.

I guess you mean like MS tranfer cable? Try to connect the drive using generic USB cable 2.5" SATA adapter, or put it in external 2.5" USB case if you have available. Also you can connect it thru eSATA if you have these kind of cables too.

I'm betting your transfer cable isn't supplying enough power for your 250g, I have an external USB-powered 2.5" cage that does that with larger drives from time to time.