I got this pitched to me a couple of months back, but why not start a Yelp-like medical tourism service? Americans can save a ton of money going to S. Korea or anther country with similar healthcare standards at the fraction of the price. It would have to be elective surgery, but you can save a ton of money.
Where does it say start time? just tells me when the campaign ends. What's the topic of the hackathon? This is all I'm seeing: http://snag.gy/YTPMO.jpg
I heard Ms. Rosenthal speak at a VLAB panel discussion @ Stanford, she didn't have anything interesting to say other than parrot the other panelist. She had a gimmicky concept with no tech background or demo to show off. I highly doubt the TV show will have real AR, it will just be super imposed post editing to make it look like people are using devices that have AR apps installed.
I'd skip the FB ads unless your product is not related to tech. Most tech savvy users have adblock and won't see the ads resulting in poor conversion rates.
For 20,000, I would spend it on a designer to make your product look great if you already have an MVP. If not, you should be working on getting an MVP and not worry about ads just yet.
An easy way for market validation would be to use a sign up page like launchrock and put in a elevator pitch. Ask friends to share on FB/Twitter and see the response.