What format is the sheet music in?
LOL That's a good one...(how about paper?)
At any rate, I did a little searching, and found a java program that will take a scan of printed music and convert it to musicXML:
It may do MIDI as well.
Rosegarden may be able to read the musicXML files and then convert them midi. MuseScore http://mscore.sourceforge.net/en/idx.php
, although newer, will read musicXML and export to MIDI.
For a WYSIWYG music editor that you can click in the notes MuseScore is pretty promising and is getting better. I have heard of others who do everything in Rosegarden as well.