I would take the lump sum and go look for work. If that happens to be with a competitor, so be it. Should your employer catch wind of it, and try to enforce the noncompete, tell them to sue you. If the do go ahead and sue you, offer them some of the lump sum as a settlement. If they don't take the offer, go before the judge and tell him or her that you need to make a living and that's what's out there. As others have mentioned, noncompete agreements are very hard to enforce.

If that sounds a little harsh, well, that's the employment market we have. Businesses look out for their own interests, you have to look for yours.