Hello, new member here... March 17 I rode NW #780, LAS-MSP on a 757.
We turned back to the gate while taxiing towards takeoff; the pilots said
that one of the computers had failed to boot up correctly. After several
minutes of repair work, they said the (new?) computer seemed OK but
that the APU would not start again and thus we would wait a bit more to
bring out the external starter equipment. It got a bit warm in the cabin
since the air conditioning was not going. Finally the A/C came on (APU?)
but the crew announced that the computer problem had returned.

Here is the crux of my question - at this point the crew said that we could
proceed despite the downed computer, but at reduced altitude. This cut
fuel efficiency, so they had the fueling folks come by to top us up. Once
in the air, the only altitude announcement was 27,000 feet. We had taken
off late by somewhere around 1:15 to 1:30, and arrived late by about 1:15,
so we seemed to have made good airspeed or had a good tailwind or did
well with air traffic.

Anyway, why would loss of one (out of multiple?) computer prior to takeoff
cause a restriction of altitude on a 757-200?