A quick question, and then a few things to try:
1) Does your screen sit flush with the phone? All the way around?
2) Take the top metal plate off the connectors, use your old screen and simply connect the two connectors. Do not install it, just use your board to boot up the LCD. Does it still rainbow when pressed?
3) Remove all screws from the left side of the logic board, including the battery screw. Your main board will stay in place by your sim card. Do you still get the rainbow?
4) boot you phone up without the back plate on, same issue?
1) If the above things do not fix the issue, I'd look at your battery and insure it is not bent or warped from being removed.
2) The battery has that little metal protector for the dock antenna connector. You are putting this below the actual battery connector, correct?
3) Take out your main board and screen, does the frame look straight?
4) Upload me pictures of the back of your phone with the cover off. I would like to see how you have it installed.
Hope something in this post helps,