This is the main sentence, "The computer on the desk broken by my little sister is mine."
Does it theoretically have two meanings?
What is broken by my little sister is the computer, or the desk?
It seems to me that both are theoretically possible.
Yes, it could have either meaning. Although I would expect that a 'broken' desk would no longer be in condition to have a computer on top.
Honestly, putting all these ideas (that the computer is yours, that the little sister broke it and that it is on the desk) into a single sentence is either going to be ambiguous or awkward. Any two of them wouldn't be too bad but all three is different.