Myti-84 plus silver won't stay on. I just replaced the batteries, but when I hit the ON button it only stays on for a few seconds then turns itself off.

Try reinstalling the OS, that might resolve the problem.

TI calculators have an annoying habit of dimming the screen when the batteries are changed so that it appears as if the calculator isn't turning on. Turn the calculator on (or at least press the ON key). Press and release the 2ND key. Press and hold the Up-arrow key for a few seconds and see whether the screen becomes legible.

To input radical numbers, you need to press the 2nd key and then the x^2 which has the square root symbol in blue above it. Input the numbers of the first radical. Hit the ) button. Then press the multiplication button. Hit the radical button again. Input the numbers of the second radical. Press the ) button again and press enter.

it could be a short on the mainbaord if it goes on for a few seconds
it could be that there is some liquid inside
i fix this calculators

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TI calculators have an annoying habit of dimming the screen when the batteries are changed so that it appears as if the calculator isn't turning on. Turn the calculator on (or at least press the ON key). Press and release the 2ND key. Press and hold the Up-arrow key for a few seconds and see whether the screen becomes legible.

If that doesn't work, add a comment to this post and we'll go from there.

what helped for me is leaving it w/h any battery's (no backup battery either) for a few days. Now miraculously it works!

That actually is a result of water damage. You probably need to replace it, or see about getting it taken apart and dried if the water damage was recent. DO NOT take it apart yourself. Go somewhere and ask if that is possible.

Double check the batteries (including the "watch battery"). Blow on the I/O port as well as the mini-USB port. This will dislodge anything that may be giving the calculator a false signal. This has worked for me.

I had the exactly same problem, and my TI 84 plus used to be extremely unresponsive and slow, as I have been fixing the latter problem by blowing really hard into the I/O plot, I did the same to fix the new problem. For many times not thing happened though. Then I insert a metal stick into it and gently hit the inside. In a short time, the calc was normal again!! Now my calc even turns on when it's been put off, with its cursor frozen. I simply use my little finger to dig/scratch the plot and see the lovely cursor beating again.

have you tried manually resetting like the manual suggests? Take out the AAA's only, hold the ON button for 10 seconds and then re-install the batteries and turn it on. If that doesn't work, I have no other suggestions.