so you want a tv under 13x13 square and under 15 deep?
somewhere around 13" is where you should look although stand height may be an issue. perhaps a model with a short base may work.
in any case, in that size range you are stuck with cheap, budget products. i would stick with a well known brand if you can but ultimately you will be searching through amazon and other websites comparing dimensions and hoping to get lucky.
mouse is correct, you seem to want someone to spoon feed you an answer. honestly we would have to search through the exact same way that you would have to for no benefit. we could give you a few things to look for (such as 720p) or recommend brands (coby or other well known budget brands) but in general such products are mass produced cheaply made crap which is a total toss up as to how long it lasts. read some reviews on a model which matches your dimensions and try to get a feel for it and thats about the best you can get.
such panels are only $100-ish anyways.