If you have a "check engine" light on, start with having the codes read. A misfire code can tell you which cylinder or cylinders are having problems. A misfire could be the cause of your engine vibration.
it cant do that because no one can stop a vibration only the earth could
no, door locks have nothing to do with check engine light.
It could be your engine mount or you might need an alignment.
battery is low or almost dead
No. It only senses engine vibration/knock.
One of the main causes of feeling a vibration in the gas pedal is engine vibration. The vibration from the engine causes the accelerator cable or linkage to vibrate and the vibration can be felt in the gas pedal. Check with a mechanic to be sure.
Not running on all cylinders? Bad harmonic balancer?
Yes it could.
Tire out of balance is the most common cause.
There are many things that can cause vibrations in a 2000 Toyota Avalon. One such cause could be a bent rim and another cause for the vibrations underneath the floorboard is the engine.
A bad rotor would not necessarily cause a bad vibration as it would most likely create a noise and wear your break pads down unevenly. It could be as simple as an unbalanced tire or a warped rim. Also if your tires are choppy then a vibration can become noticeable. Also a bad bearing or axle could cause vibration (however, it would be noticeable at a lower speed).