My co-founder and I are applying without a link to a demo.
We've been working on hard problems and architectural things that need to be ironed out before features can come. Also, our idea has changed a bit...
I just think your odds are much better if you demo something. Realize that some of the guys you're up against can produce a working web application that does something useful in a few hours. So, mock something up.
Make a demo. How else can I say it? Demo something!
I too am applying with a large hard problem, but nonetheless I'm going to have a demo. It's a throwaway prototype that, if I tried to use it as production code, would scale to about ten users before the server fell over. See if you can figure out a way to do the same. If you're doing a put-your-favorite-UNIX-command-on-the-web type startup, just make a web-based frontend that actually invokes that UNIX command to do its processing.
I would also like to take this opportunity to ask if there is a point for single-person applications.. the faq's say the chances of getting funded are far lower, would this be a non-issue if the applicant is willing to partner with another person/team?
("find a cofounder" is what pg will probably tell you; it's what he told me repeatedly before my interview. it was a big time investment to find the right one, but completely worthwhile. couldn't imagine going through this alone, and it only gets harder to get a cofounder the longer you put it off -- it no longer feels like 'their' idea.)
Are you sure you aren't making excuses? Change the problem if need be, I say.