I looked up a trademark on TESS and it turns out that it is already trademarked. This may sound like a noob question, but can I use it if my business is completely unrelated ? What if I own the domain, but someone else owned the trademark.
Yes, trademarks can be shared as long as they do not cause confusion.
Lexus the car Lexis the information service (Spelling is irrelevant in trademarks).
VAX a vacuum cleaner. VAX a computer
Which worked well until the vacuum cleaner started running ads "The VAX sucks."
Ace Bandages and Ace Hardware. Delta Faucets and Delta Airlines.
Since these are in unrelated industries, there is no confusion. So, there is no infringement.