Daniel,
When it comes to getting grants, the bottom line is to hire a professional grant writer. I work with one and she has made the diff between getting a grant and not getting one. The world of securing grants is so twisted and convoluted as to boggle the mind. It is not simply a matter of just 'filling out the forms'. Even the suggestions of Videoman about getting local businesses to underwrite equipment, is tricky as they will want the gear returned in the exact same condition as loaned. So you'll need production insurance to cover the cost of the gear should it get damaged. Another thing to consider; local business will expect a return of some kind for their efforts. You'll have to be creative in coming up with something that will get them interested in lending you what you need, but not put you in the poorhouse!
Know that charitable organizations are not 'charitable'. They have very specific agendas they are pushing and what you are doing will have to be exactly in line with what they want to portray. They are not going to spot you the cash to make your 'thing' that has nothing to do with theirs. Same goes for getting grants. A pro grant writer will be able to sit down with you and help you craft your project to meet the guidelines to what the Grantor wants to see in your proposal. Also, if you do get any money nearly all production grants are there for 'finishing' fees to help you get your project completed, not finance your project. They always expect you to have found other moneys and that theirs is the last money in.
You can see it for yourself on PBS' Producing for PBS section on their website. There will be listed some of the basic stuff that will be in a proposal for a potential PBS program. Then look up Funding and there you will find some of the usual funding sources by which many of the programs on PBS get their money. You'll need multiple sources so depending on how large your project is; you may need a lot of different grants.
Obviously, getting grants is possible. But you're going to need professional help to get them.
