My iPod Touch 4G screen cracked while playing, and so we had to replace it. I bought a screen replacement, and decided to do the work on my on. So I fixed the new screen, as directed on a guide on iFix it. From then on, it would work fine, except once in a while a series of white lines would appear, completely covering the screen. You could see only about 20-30% of what was going on on the iPod, the rest was just white. This could be fixed by just tapping, or turning or shifting the screen a little. One fine day, the screen went permanently white, and no matter how much I wiggled or moved the display cable, it would not get back to normal.
After a number of days, I decided to buy a new screen, and replace it. I re-did the procedure as before, and turned it on. The first time, the screen appeared VERY dim, barely visible, even though the brightness setting was at maximum. I thought this was a problem with the alignment of the display cable, and so without switching off the iPod I disconnected and reconnected the display cable. The iPod has not turned on since, and I know this because I have tried a hard reset, but it does not show up in iTunes. Also, I tried connecting it to a charger, but in vain. Could this be a Power button failure? Or Home button? Or something with the logic board?
Please help, thank-you.

I would say that maybe you've damaged the power flex cable, with the screen out, trace the flex cable from the power switch which should also run to the volume control side and then up to the main board, if I'm correct then it will be damage somewhere (note: even the slightest hairline cut is enough for it to not operate correctly).

Definitely check the flex cable pull up the aluminum plate that covers the board usually what happens is when you pull up
The board to disconnect the digi cable you can rip the volume/power flex it has happened to a lot of us I will work on a way to jump it without the power button should get back to you in awhile