Good points, and it looks like we both hit on the inverter being the
likely source of the problem, but, as you wrote, the one-minute time
is strange.

If the backlight was marginal and the display pinkish, I'm sure the
OP would have mentioned that.

To see how to open up and make repairs to the 510m, the owner's manual
and service manual are here:

<support.dell.com/.../index.htm>