Its not 100% clear what you are trying to do, partly because you say you want to get the data from the computer to the arduino via MIDI.
Are you trying to download the midi file onto the Arduino and then have the arduino play the file autonomously?
Are you trying to get yor PC to read the file and then communicate with the arduino?
Are you trying to get the steel drum to behave like a intelligent instrument with a MIDI interface (i.e. the computer is not really relevant)?
There are lots of ways to skin a cat.
I don't know the exact format MIDI files are in, but you should be either able to read that format directly on the arduino or perhaps use your computer to pre-process the MIDI file into a simpler format of your own for the arduino to use.
Likewise if you want to communicate between the computer and the arduino you could make up your own messages and communicate them serially.
Alternatively you could look for exisitng products like this https://www.sparkfun.com/products/9595
which may do some of what you want.
One way or another I would say what you want to do is possible and the cost for the interface end will probably be quite low.
You will also need control and power for the solenoids.