It sounds like the system had either a liquid spill or the battery swelled, so the keyboard and trackpad are messed up.
Often times I find the cable or the trackpad has suffered the most damage. Unlike the Pro systems, the Airs share a single cable connection to the logic board from the trackpad. You’ll need to pull the battery to inspect (replace) the cable [product|IF108-031], then I would try replacing the trackpad next [product|IF108-029] following this guide [guide|10443]