Make sure that all keys are traveling freely. Maybe they are gunked up or there is something under them preventing them from functioning correctly.
Orient the keyboard verticaly and gently tap it to dislodge eventual debrits.
If keys are gunked up, they may start auto-repeating if you perss them frimly. In this case, you need to remove the key caps and wash them. Just don't have any water splash on the keyboard's base.
In what conditions was that laptop stored. Maybe there was to much humidity and the key's contacts started to corrode. Try pressing a key a few dozen times. Does it start to respond. If yes, do the same with all problem keys.
Maybe there is some corrosion on the contacts between the keyboard and the motherboard.
You need to open the case, then, disconnect and reconnect the keyboard a few times.
Maybe you just need a new keyboard. The simplest way is to simply connect an USB keyboard, although you'll loose on the mobility aspect.