boot problem with emachiens t6420

Power up Problem
i have an emacheines computer and it will power up but it won’t boot direclty without a keyboard in the ps2 input.
the way that it does boot up is if i attatch and detach the mouse several times to get a connection.
the way i can tell if the computer will boot is when i see that indicator lights flash on five seconds after i turn the power on.
so i know it cant be me needing a new motherboard or power supply because everything works fine and is operational ie… cd/dvd roms usb inputs so on and so forth.

also a usb keyboard wont do the trick until after the system is started up.

need help. does anyone have an answer?