The only other things I can think of trying:
Sometimes a battery will bulge/expand and affect the keyboard/trackpad. A visual inspection is needed to observe this by removing the bottom cover. Do not do this if you're not comfortable with it. Given that it works in Safe Mode, I don't think this the case though.
Backup your data, preferably twice, once with Time Machine, and once with Carbon Copy Cloner.
Reinstall the OS: https://support.apple.com/en-us/HT204904
If no luck, erase and install a new OS, then try it out before restoring any data or apps (again, backup before erasing the HD): https://support.apple.com/en-us/HT201314