Sand off loose paint, prime with a good primer - I use Zinsser 123 and topcoat with a good cabinet paint. I am just curious - how old are your cabinets.

The touch up probably won't work. A repaint would be needed...but your requirement of "won't break the bank" is going to be the part that gets you into trouble.

Is it possible to simply leave the home "as-is"? What does your realtor suggest? Some areas show a hot housing market and the appearance of the interior is secondary (Vancouver sells condemned houses for $120K OVER the asking price...definitely no updates done when there is plywood for windows). Other areas have slow sales where every extra bit of effort counts.

Without knowing where you are, and not knowing your budget, it is tough to make a suggestion. A full paint job (professionally done) can start around $7K. For some this is "breaking the bank" for others that simply cash out a few bonds and they money is in their account 3 days later.

The return on a kitchen paint job (in your area) might be as high as 65%....or as low as 0% (the price agreed upon being so low that you could have saved the money and left it alone). You won't get all of your money back. Is it worth it to you?

A local realtor will help guide you through these decisions.

is this the only door this happened to? from towels hanging over the door? if so i'd try to paint just these doors.

if its the whole kitchen, well, hmmm.

but in any case, tweak the hinges so the doors hang even.