Hey,
Its sad that your 2 prime sponsors left you. Now some of the demands might be a out of way, tho i am pretty sure you are great competitors and will come up with a way to go through this setback.
Though i will say that correspondence with companies is very important, now you can send e-mailes which is very simple, or faxes, or a phone call for more impact. Jus keep it simple and professional and tell the sponsors or companies your needs upfront. Like if you goto a big company dont go and ask $200. If they are interested go to them, give them a small presentation and say "Hey, we need to do this competition and we need $2000 or what evver from you and these are the benefits you get". And also have a budget so they know where their money is going to go.
A big pointer the advertisement your sponsors get form you should be based on the money the provide, so if someone give $200 they shouldnt get a logo as big as the one who gave $2000.
Though my experience suggests its all about being at the right place at the right time.
I hope you benefited from the above giberish
Regards,
Abdullah Ramay
Team Leader