e1ven is spot on. You can't screw around starting a business with indeterminate revenue potential if you have dependents. You need to have a years worth of frugal living expenses in the bank (including paying for health insurance out of pocket) before taking that kind of risk.

Work on your business part-time, or put in some extra hours at work to increase your rate of saving for the eventual day when you can quit. It is possible to build a business part-time. It's harder, the odds are stacked even higher against you, and you get a lot less done. But you get to keep your family fed and your health/retirement benefits in place and working for you.

pg covered this in his "Why not start a startup" talk. Every reason except "you have a family to support" he debunks. This is the one that can't be debunked, because starting a business is not guaranteed. It could take months or even years to start seeing revenue, if you ever see revenue. A few grand from YC only makes a few months difference, tops, in the "when do I run out of money" equation. If you aren't already quite confident you have the money in the bank to last until you can make your business pay or at least be sure it's not going to and you can feel good about going to work at a regular job, you aren't in a position to take that risk.