Xperia u dont turn on just red led blinking after charge up

I experienced the very same problem twice.
The red led would either stayed on all the time when charger was connected or it blink whenever I'd push the power button on the phone, but the phone would not turn on.
My solution was to unplug the charger, take out the battery and the sim, keep them separated for at least 48-72 hours, then put back the battery, connect the charger again (don't use your computer's usb port, use a real wall charger, preferably the original one), turn on the phone.
If it doesn't turn on immediately, let it charge for a few hours and then try to turn it on.
I revived this phone twice using this method, first time I thought I was just lucky, but apparently it's reproducible.

Hope it works for you too.