"There are" is a plural form, and should not be used when only one thing is mentioned. For example
There are a television in the room. 
should be
There is a television in the room. 
Now with the example sentence:
There is a table and a chair in the corner. 
two items are listed, but they are listed as two separate items, not as a group, so I would use the singular form.
I would use the singular form because I would treat it as a reduced parallel construction, short for:
There is a table and there is a chair in the corner. 
In a parallel construction, the verb is repeated, or when it is the same verb, is omiotted but is assumed to apply separatly to each element. Thus in the example, I would treat the verb as applying separately to "a table" and "a chair", and so I would use the singlular form "is".
If the example is rephrased to:
There are a table and chair in the corner. 
I think "are" is correct, because "a table and chair" is a single group consisting multiple items. Dropping the repeated article makes the plural form feel more natural to me. But you will find native speakers using both "There is" and "There are" in this sort of construction.
There is a computer and a TV in my room. 
could be considered a shortened form of:
There is a computer and there is also a TV in my room. 
The idea that "there's" is correct when neither "there is" nor "there are" would be correct strikes me as simply wrong. The word "there's" is a contraction of "there is". It is sometimes used, quite informally, as if it were a contraction of 'there are" as in:
There's five people waiting to see you.
But usually it simply represents "there is" and is not correct when "there is" is not.
two items are listed, but they are listed as two separate items, not as a group, so I would use the singular form." If they are listed as two separate items I don't understand why using "are" is wrong :( Could you please explain?
– Antonia A Nov 24 '21 at 09:07