It could even be rephrased to be a little more technically correct:
The software installation will begin when the computer is ready.
This correction goes for both instances of your phrase, since they both (kind of) indicate that the installation will be instantaneous - for example, depending on the computers readiness, that is when the software installation process can be decidedly successful / complete. If you're in a different situation then could you explain it in a little detail?
My reasoning for the latter being invalid is simply that it sounds plain wrong, inasmuch that 'when the computer is ready' is your condition for installation, 'when the computer will be ready' has a condition within a condition that can't necessarily be satisfied. There'll be technical terms, to be sure - but no doubt a linguist will notify me.