Leave the phone plugged to the wall charger (not connected to a computer by USB) overnight, and try to power on again. Try both regular power on, and bootloader. Try these while the charger is connected (as well as not connected), also.
There is a known bug with the phone, where it can sometimes be difficult to power on after draining to shutdown. You may be experiencing this bug, rather than anything to do with the ROM install. Especially if you didn't experience any other bugs for a few days after the ROM flash, I would tend to think it is not the fault of the ROM.
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Phone: HTC One X (AT&T version) Rooted, Bootloader Unlocked, S-Off
Tablet: Samsung Galaxy Note 8 (WiFi only) Rooted