Dave, I hope your computer is an IBM-type and not an Apple product. Here's how the system works on my own computer (Windows 7).

Let's say you have converted the abc file at the mandolin tab converter and are seeing the notes.   

Click on MIDI below the notes.
Save the file with a sensible, one-word name at My Documents
Open Windows Media Player. (You may have to use Start to find it.)
In the Media Player box, choose Other Media
I hope this opens an alphabetical list.
Choose the title and play.