I like the idea. I'd definitly get on the band wagon if there was something like this.
1) for alot of hobby builders that I know (including myself) I could probably build a $1000 dollar robot (or less) but then may not be able to cover entrance fees. Perhaps a sponsorship in this area, rather than parts or money for the actual robot, could be allowed.
2) The idea of corporate or university sponsorship for the event as a whole, as has been suggested, is a good idea. This will cut down on required costs of the organization putting on the event.
3) about universities...I think that having the parts and build methods accountable for would help in this case, but leave equipment out of the restriction. Alot of universities or technical schools will let you use thier labs if you ask nicely, tell them what it's for, and give them a background on what your doing. This doesn't mean they can give you parts, or even expertise from professors and such. Just that you can use thier equipment if you need to.
Case in point: Have a rule that parts must be traceable. Either through reciepts, bills of lading, or soemthing to that effect. Something to make sure that a team can prove that they obtained the parts themselves rather than having them donated. I would allow "part swapping" though. soemthing like "I'll give you this ADC for that DAC" or something along those lines. But make sure that trades are for fair value of a single piece. Not an op amp for an embedded GPS module, but say a binary comparator, op amp or two, and temp sensor for a multichannel ADC. (I think thats about $10 of value for the swap or so...that's the gist anyways)
As far as build methods, require each team to keep a journal of the build process, including who came up with what idea, thier theory behind it, and have them able to explain how they came up with it and made it work. That could keep someone from getting something cutting edge from a university or whatnot, and know how to implement it, but not how it was built.
4)Make everyhting open to competitor scrutinization after the competition. This will keep things from happening like they used to in formula one, where one team has a tech advantage and keeps winning for a number of years straight, until someone else catches up and takes over for a few years. It will give people ideas for the next event, develop camraderi between competitors, and make it a learning experience from someone elses success, not jsut your failure. In this respect, everyone could come away a "winner", not just the winning team.
5) Instead of one task, make the competition a multi event type of thing, where one robot, with one configuration, and no parts or software changes between events, must compete in a number of different tasks. This will also help keep one machine from dominating because a machine vision robot can choose a colored ball better than a robot built for transporting things, but cant necessarily be as good at transporting things from one place to another successfully and autonomously.
Just my..uhm..5 cents ;)