PayPal has a Buyer Protection Policy, but I've never had to use it, so I don't know how well it works for items that are "significantly not as described". I assume you will have to return the item to the seller to get a refund. PayPal does have more of a personal touch in these cases than you might expect (the people who work on your case will actually talk to you), so be nice when you leave messages to the seller and have your evidence ready (photos, Delivery Confirmation number, etc.).
Your credit card company might also have a purchase protection plan, but only if it's part of their service agreement.
Keep in mind that most sellers on eBay are not professional retailers (they do other things with their time), so don't expect an immediate response to your messages. Three business days is pretty standard on eBay, and I think disputes allow about seven days for the other party to respond.
I suggest that you wait until you hear from the seller before you return the projector.
You didn't say the projector was damaged in shipping (based on your phrasing, I assume it wasn't), but I would like to clear up a misconception that a lot of people seem to have. The buyer cannot file an insurance claim if an item is damaged during shipping. Only the person who gave money to the shipping company (i.e., the seller) can do that. The shipping company won't even talk to the buyer since their business is strictly with the seller. The seller is their customer, not the buyer. If the seller does not file a claim, then the shipping company will not give any money to anyone. Normally, the buyer has to send the damaged item to the shipping company, they inspect it, and if they approve the claim, they send the money to the seller, who should then reimburse you. If the seller won't even talk to you, then you will have to rely on PayPal or your credit card company to deal with the problem.
By the way, I would like to reiterate that you need to allow some time for the seller to respond. You say you received the projector today and you opened a PayPal Dispute the very same day. Speaking as a reputable eBay seller who has to deal with problems on rare occasions, I have to say that I would be a little pissed if a buyer couldn't wait for an answer for more than one day before opening a PayPal Dispute. A Dispute should only be used as a last resort if you don't get satisfactory results in, say, about a week. If you're dealing with a good seller who sells stuff on eBay part time, you are making it harder for him or her to help you. PayPal Disputes are a big annoyance when a seller wants to help a buyer, and in some cases they probably aren't necessary at all.