Ok, reading this thread, thought of it, if this is a quasy fan film and you yet to be able to get permission to do this with the original series, for funding (basing you can't get permission, etc) for a 'fan film' here's a few outlet you might be able to try...
First get yourself a budget/proposal written, yes, it would be helpful, at least to have a rough idea of how much you need and what is needed etc.
2. contact all your friends and such to round up all the talent needed for each department, then deduct their cost value off your budget list so now you ended up with a more realistic to get amount
3. see what else you can get for 'free' or 'volunteer' so again, it will help trim down the amount, of course, always add in a 20% constigency (or more in case need it)
4. talk to those people you are most friend with, present them the idea and see what they think (I personally like the direct face to face or phone approach when asking money from friends, but some people gets offensive), those who you have professional contact with, a letter is better than an email request... Set up a donation packages, like for $100, what you get in return, as you mentioned and this is based of a fan film, it's harder to get investment but rather donations. And keeping in mind with copyright concerns, your finished project can't be played at any festivals that are charging money for people to come watch, and you are expected to give it out freely the finish product so most 'investors' rather to be called donators that would help clear the 'mudded' copyright concern.
6. solicitate as much donations as you can, make sure every letters/written documents has the mentioning of fan film and it is not for sale/profit, so it would make it easier pitch, think of this as a fundraiser for a nonprofit org.
7. if you have previously worked clips, have them readied when you approach friends/network of contacts who yet to know your talent, your previous clips/work would help them be interested.
8. don't stop begging
or max out your credit card.
9. If all fails, go bck to 1.
Johnny