What holds up home computer? (5)
I believe the answer is:
brain
'computer?' is the definition.
(a computer is a mechanical 'brain')
'what holds up home' is the wordplay.
'what holds up' becomes 'bra' (a bra holds up breasts).
'home' becomes 'in' ('he's home' can mean 'he's in').
'bra'+'in'='BRAIN'
(Other definitions for brain that I've seen before include "Haemorrhaging of talent" , "Thinking organ" , "Intelligence" , "Intelligent person" , "Clever type" .)