Although they're different words if personal computer isn't accepted and it's saying my computer then it implies you don't have it.
That would be "to jest mój komputer." Whenever a sentence in Polish goes "this is" the form of "this" is always the neuter nominative singular "to." Since the word "this" is masculine singular (ie it agrees with komputer) we translate it like an adjective, since that's how it's being used. Jasne?
I expected "mój" to become "mójem" because of "jest" governing the instrumental case... I guess it doesn't apply to possessive pronouns!
1) possesive pronouns are like adjectives
2) instrumental mój is moim -
ten złom jest moim komputerem - this junk is my computer
Most of such contractions are accepted automatically, but not the ones like "noun is = noun's", it seems. Sure, I can add it. And "that", of course.
In the previous one, I had "My dad's bed is white" which translated to "Łóżko mojego taty jest białe" which lead me to think that the item that is being owned comes before the owner. So why isn't "Ten komputer jest mój," "This is my computer?"