Hi Keith about your only recourse with the RCA tablets is to do a factory reset ( which will be located in the Settings portion of the tablet). The RCA tablets are known to have issues as they are a relatively cheap tablet. If that doesn't work for you, you don't really have much else you can do, my recommendation is in the future when you're buying a tablet spend a little more money and buy one of the name brand tablets such as Apple or Samsung.
So I'm going to just throw this out there because it doesn't seem to be covered when you plug it into iTunes does it show that your phones in recovery mode or does it show that your phone is on? If it shows that your phone is in recovery mode have you tried a hard reset? Also have you disconnected and reconnected your battery after the screen replacement? I've done thousands of iPhone 6 screen repairs and I've never once blown a backlight. If this is an iPhone 6s it's a different story. But an iPhone 6 it's highly unlikely that it's a backlight filter.
Hi, sometimes if you can get into the recovery menu it Will allow you to do a factory reset which sometimes can solve the problem. If that does not work it's looking more less like you're having a problem with the NAND chip on the motherboard in that case it would not be replaceable and it would be time to get a new phone. To get into recovery mode just google recovery mode HTC M7 and it should give you the steps to get there.
I agree with Brian take it back, and make sure to ask if they are using premium parts or aftermarket. There is a huge difference between the quality of the two and the aftermarket's, while they may work are not nearly as reliable as a good OEM Refurbished screen.
Unfortunately it sounds like a motherboard issue and typically on Blu phones your better off replacing the whole unit then trying to fix. Only chance you may have is if the phone is less then a year old and you should be covered by there 1 year manufacturer warranty, though it may take a couple weeks to get them to replace it. Just look up there website and there should be a place to submit for warranty. Good luck!
We have done 5 of them all the same problem Update (05/03/2017): Do you see the little black square near the ear speaker hole? (Well it's supposed to stay on the prox sensor). On the 7+ for whatever reason it stays stuck to the screen most of the time. It must be transferred over or you will end up with problems as the prox is shorting out. We beat are head against the wall for weeks over this issue and finally this so simple answer, that we were missing solved our problems.