K.M.
A.,
I have the exact same problem with my 3 1/2 year old daughter. We tried all the things that you tried (promising dessert, time outs, etc.), and it's only dinner we have trouble with (seems like it's a common problem). What we decided to do just this past week was not try to force the food down her throat. She has to eat what we eat and she does - for the most part. But rather than forcing her to eat and having it be a constant struggle, we just let her be excused from the table when she asks and when she says she's done. She's not going to starve and if she asks for a snack after she hasn't eaten what we think is enough... she can only have fruit or veggies; if anything at all. So, she will choose to eat dinner when it's in front of her, or she has the choice of less appealing things (at least to her) and they're healthy choices. Just a suggestion... hope it works as well for you as it has been for us.
Best of luck!
K.
Just a suggestion.