While the overall tone is good, your proposal could be strengthened by including something you would do in addition to the subsidies you are looking to receive. I'm definitely not doubting your good intentions here, I just think it is very easy to sound sincere without actually contributing anything.
My parents didn't believe that funding a higher end computer for me to fold was worthwhile. Being results oriented, they did not like the concept of, "we now have a slightly better understanding of how X behaves". They told me to work for it if I really believed in it, so I did. Show your determination by investing something yourself. Even if you don't inspire your immediate audience, friends might see your passion and donate old hardware to you as they upgrade. Every point counts!
Seeing as your current schedule is already hectic, maybe you could pledge to be more frugal and contribute x amount per month or per week to fund this project. Showing this type of dedication and commitment would definitely make a stronger case. In addition, it would be great to show them a plan of what you want to build and a rough estimate of costs to assemble as well as upkeep. You touch on this briefly by stating that you have spare hardware but don't have enough pieces to complete a system. Let them know what these missing pieces are, and show them that you have not only thought this through but have put in a lot of effort into it already. Even if they end up saying no, you've done the planning part already which you can and will use later on when more funds become available.