Hi Scott,
You know, the thing is, Apple won't even repair an iPad; if it's under warranty it'll just be replaced, and otherwise the best they'll do is offer you a trade-in or discount on a new one.
You have probably run into exactly why they don't repair them; the fact that removing the screen is not always successful. The thing is, there are delicate electrical connections between the flex cable going to the motherboard and the glass that the LCD circuits are printed on. Those connections, once disrupted, cannot be repaired and the only fix is to replace the screen.
It sounds like that's what's happened, whether it's from maybe inserting your opening pick just a millimeter too far, or even just the screen flexing as it's removed we'll never know, but my best guess is the screen is toast.
Really, about all you can do is open it back up again and check the connectors on the motherboard. It's sometimes possible to get them pressed in so it seems like it's seated, but isn't really, so unplug them all, check them over carefully with a magnifying glass and a bright light looking for any bent, broken or missing pins. Bent pins can sometimes be straightened with fine tip tweezers, but broken or missing ones are obviously more problematic.
Assuming everything looks good, clean both sides with 90% or higher isopropyl (rubbing) alcohol, give it a moment to dry and plug it all back in. Power up the screen before reassembly and see if anything has changed. That's going to be your best bet at getting it working before ponying up for a new screen.
If you do need a new screen, the cheapest parts I know of would be either look at AliExpress.com for new ones, or eBay for used and aftermarket ones. But try reseating the connector(s) first, as those FPC connectors can be tricky to get seated correctly and could well account for the problem.
As far as it not powering on, is there any sign of life? Is it recognized when plugged into a computer?
Give these suggestions a try then come on back and let us know what you found.