Re: "There is a computer and a TV."
Native speakers tend to go with "There's" at the start of such a sentence. We use "There are" before a plural noun, more than one plural noun, or a plural noun followed by singular nouns.
There's a computer and a table in my room.
There are two computers in my room.
There are two computers and three tables in my room.
There are two computers, a table and a desk in my room.
"There is" sounds unnatural to me in the first. That's probably why we contract it to "There's" which, in BrE at least, can serve as "There is" and "There are".
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.