Rather than replacing things based on assumptions, you need a plan to figure out exactly what is faulty. And a replacement/repair process that is known not to introduce new faults.
So, first of all.... Don't change any electrical item whilst the power is on. Unless you have enough electrical/electronic knowledge to know it won't damage something else. It may seem a bit tedious and slow to turn the power off every time you change something, but it may be quicker in the end. (You might already have fixed this yourself, rather than waiting hours for someone here to figure it out!)
Second of all... Stop and think. First diagnose the problem, *then* fix it. If the X axis motor is not doing what you expect, what could be the problem?
Thirdly, try to be precise in describing what's happening. You don't say whether Y axis motor is vibrating when you try to print, or right after rebooting. Please describe the exact sequence of actions from powering on until the motor starts vibrating. (e.g. turned it on, loaded standard "5mm calibration cube" model using Repetier Host, hit print button. Y axis motor started vibrating when the printer tried to home).Any other strange symptoms?
One approach would be to simplify things.... if the X-axis is doing something odd, isolate it. Try turning off all the heaters and fans and things and move just the X axis. If it still doesn't work properly, disconnect (after powering off) everything except the X axis and try again.
Another approach would be to assume that only one thing is faulty. So replacing one item at a time with a known-good item should fix the problem. So, if the X axis is faulty and you suspect the motor, try swapping the X and Y axis motors. Does the problem now move to the Y axis? If so, it's the motor; if not, it's one of the other things in the X axis. To speed this up, you could just try swapping the X-axis plug to the Y-axis socket, and vice versa.
From what you've said, the problem isn't the motor (replacing the motor with an assumed good brand-new motor didn't fix it) and not just in the X axis (the same thing now happens on the Y axis). So, what's common to the X and Y axes.... really it's just the controller board, RAMPS board, and power supply.
Because it's quickest and easiest, go round every 12V connector and motor connector and make sure it is plugged in properly, then try again.
Next I'd check the power supply and make sure it's putting out enough volts and amps. If not, why not? Faulty power supply, or a short (perhaps intermittent) almost anywhere in the 12V wiring. Then I'd check power at the RAMPS board and controller board... 12V supply & 5V supply.
Next (mainly because you had weird things happen with the LCD) I'd try re-flashing the controller board... again easy to do, and it verifies that a whole lot of things on the controller board work.
If none of those things fix the problem, get back to us here.