Replaced screen. Now no power.

There are two potential scenarios here:

The first one is a backlight or LCD issue

It’s very important to always disconnect the battery before disconnecting/reconnecting the screen assembly. The issue is that the LCD connector has pins that have high voltages (i.e. the backlight is ~20V) and ground in very close proximity. When you fumble around trying to line up the connector plug to the receptacle, you can short out the voltage rail and cause damage to the components in the backlight circuit. If you’re lucky, then only a backlight filter is damaged but other times, the entire circuit could be affected. Either way, this type of repair requires micro-soldering and isn’t really a DIY repair.

To test for this, plug your device into a charger or an iTunes enabled computer. Then shine a bright flashlight on the screen. If you can see a dim image, then the backlight circuit has been damaged. If you can’t see an image at all, then it may be the LCD circuit that is damaged.

 You can connect the original, cracked screen to confirm this. If the original screen has the backlight on, then the replacement screen has an issue. If the original screen also doesn't show the backlight, then the backlight circuit is blown.

The second one is a “dead” device

Start by disconnecting the battery first (always!). Then disconnect the screen, front camera, rear camera, buttons etc. If you have access to a multimeter, you could measure the battery first. If it reads ~3.8V - 4.2V, then it is good. Now re-connect the battery; you should only have the battery and Lightning Dock flex connected. Connect a known-good, preferably Apple-original Lightning cable to an iTunes enabled computer.

Does iTunes recognize your phone? If so, then you should re-connect one flex at a time (don’t forget the battery!) until the phone stops working. I would start with the buttons first, then add the cameras and then the screen.

If the bare-bones setup does not get recognized by iTunes, then you most likely have a logic board issue. You could send it (or find a local) to a repair shop that specializes in micro-soldering repair. Sometimes the fix can be straightforward (i.e.  a blown filter) and relatively economical.