"desk computer" is correct and can be used in written English.
You can use it to refer to a computer that is typically found on or in a desk. For example, "I'm typing this email up on my desk computer."
He works with a desk computer, a small adding machine & a Stock Exchange ticker.
Sandy sent water surging to six feet at the lobby entrance, wiping out the building's electrical systems and destroying its cafe, admission desk, computer system and gift shop.
Even with a desk, computer and chair arrangement that complies with Occupational Safety and Health Administration recommendations, how many of us still hunch over our keyboards?
Much to my surprise, he wrote me from his computer class at school while I was working at my desk computer.
The Library entrance was moved from the fourth to the main floor of Langdell, where users also find the Circulation Desk, computer classroom, microforms, and current legal periodicals.
"Please send whatever you can!" The water surged to six feet at the lobby entrance, wiping out the building's electrical systems and destroying its cafe, admission desk, computer system and gift shop.
And say "desk computers" instead of "desktops"?
Technology has changed, too, allowing people to job-hunt or devise new business plans untethered from their clunky desk computers and tangled-cord home phones.
She attached a small scanning device to front desk computers at the two resorts.
The shabby office, five flights down from Hillary Rodham Clinton's campaign headquarters, is scattered with desks, computer terminals, televisions, hanging cable wires and telephones.
Everything else is looted or broken on site: chairs, desks, computer screens and computers, standing fans, and documents are taken.
