Plug the phone into the computer. Copy a file or two. (Note where you're copying it to on the card - which folder. Making a folder named Music would make sense.) Eject the phone from the computer. (This is important. Windows does "write-ahead". When you "write" a file to the SD card [or any external device], Windows sets the file up for writing. Then it does he actual write between other operations. If you just remove the phone, the file may not yet have been written. Ejecting the phone forces Windows to finish writing the file first.) Turn off USB storage. (The phone can't see the SD card if USB storage is on - the card is "switched" to the microUSB port.) Run My Files (or any file manager) in the phone. Look on the external SD card (if you're still running Gingerbread, that's the only one you have - if you're running a later version of Android you may have an internal SD card and an external SD card) and look in the folder you put the music file.
Three other possibilities:
1) The music you're copying is DRM-protected. You can't copy DRM-protected music. (That's the point of DRM-protection - you buy the right to run the music only on the computer it was originally installed on.)
2) The file format is something the phone's music players can't read, like .aac. The file is there, but it's like a document written in a language you don't know - it can't be used.
3) You're copying shortcuts, not the original file. A shortcut is just a little file pointing to the actual music file, it's not the music file itself.
(There could be other things I'm not thinking of.)