If all goes well, NASA's Mission Management Team is expected to give shuttle commander Rick Sturckow and his crewmates permission to seal the hatches between the station and the orbiter late Monday in preparation for undocking Tuesday.
Ground controllers also tested a new solar array rotation system overnight in preparation for switching over to normal sun-tracking mode.
Four of the six computers that crashed have been back online since Friday, reports CBS News correspondent Peter King. That's by design, with the other two on standby. Most of the systems that run on those computers are back, too.
The mission managers will test the rockets that keep the station aimed properly. They want to make sure the computers can do the job, and that the U.S. and Russian computers can talk to each other.
Atlantis has been at the space station since June 10.
During the computer meltdown, Atlantis' thrusters were used to help the station maintain its position. The space station's thrusters haven't been used since last week.
Atlantis is currently set to undock on Tuesday and land Thursday in Cape Canaveral, Fla.
"We will have sort of an extra double-check, if you will, to make sure everything is running well," flight director Kelly Beck said of Monday's test.
The Russian computers, which also control oxygen production, crashed last week. All six of the computers' processors were back online as of Saturday. The two processors that took longer to revive are now on standby mode and can be used if needed.
Except for an oxygen generator, all the space station systems that were powered down when the computers failed are now running.
Also Monday, Atlantis' crew was to finish packing the shuttle for its return trip to Earth. The shuttle and space station crews were set to say their goodbyes before hatches between Atlantis and the outpost are closed in preparation for Tuesday's undocking.
On Sunday, shuttle astronauts completed the fourth and final spacewalk of their mission to continue the construction of the space station.
During a nearly 6½-hour spacewalk, astronauts Patrick Forrester and Steven Swanson activated a rotating joint — their top priority — on the outpost's newest segment so a new pair of solar wings can track the sun and provide power to the station. The solar arrays were delivered to the space station by Atlantis.
The astronauts also set up a new camera stanchion outside the station's newest segment and a computer network cable between the U.S. and Russian sides of the outpost. They were not able to bolt down a problematic debris shield and instead secured it in place.
While the seven-member crew of Atlantis and the three-man crew of the space station spent Father's Day 220 miles above Earth, the holiday didn't slip the minds of the nine fathers at the outpost, who collectively have 24 children.
"Happy Father's Day to everybody downstairs," said U.S. astronaut Clay Anderson.
CBS News Space Consultant William Harwood has covered America's space program full time for nearly 20 years, focusing on space shuttle operations, planetary exploration and astronomy. Based at the Kennedy Space Center in Florida, Harwood provides up-to-the-minute space reports for CBS News and regularly contributes to Spaceflight Now and The Washington Post.