1) You have given good diagnostic information ... except brand and model number of water heater are missing.
Locate this information on label on side of tank.
2) 2 flashes for high temperature indicate you have Whirlpool or Craftmaster Energy Smart.
You have dual element 240V tank-type electric water heater with electronic control board and temperatures sensors.
Sensors can be ordered separately for $30 each.
Sensors seem like best suspect since elements test out and you have new control board.
3) Did you test elements for short to ground through center of element?http://waterheatertimer.org/How-to-test-water-heater-element.html
4) Energy smart requires 10 gauge wire and 30 amp breaker. If wire or breaker are undersized, then I would expect chronic problems with electronics. I believe the requirement is so element draw or other factors don't starve electronic control board.
5) How it works: Energy smart is non-simultaneous water heater. Non-simultaneous means upper element turns on first. When upper temperature sensor is satisfied, control board cuts power to upper element and sends power to lower temperature sensor and element. So both elements are never ON at same time. Lower element runs until lower temperature sensor is satisfied. I do not know decision tree for how microchip processes the information.
6) I have examined this water heater and read the manual. I wrote following page, but have not conducted electrical testing on unit simply because it is controlled by micro-chip.http://waterheatertimer.org/Whirlpool-Energy-Smart-electric.html
7) Sample Energy Smart manual:
Manual does not show how to test temperature sensors, but manufacturer might have more information. Manufacturer might have information how changing meter can affect their electronics.
I would guess undersized wiring would have greater impact than electricity turning off for 1 minute.http://waterheatertimer.org/pdf/Whirlpool-energy-smart-electric-manual.pdf
8) 4500 Watt elements should test 12.3 ohms, so your elements check out fine.
Be sure to test for short to ground by setting multimeter to ohms, remove wires from element, and test each screw to bare metal part of heater and to metal base of element.http://waterheatertimer.org/images/ohm-reading-for-emements.jpghttp://waterheatertimer.org/How-to-test-water-heater-element.html
9) The water heater industry changes very fast, so current manual is best place to start troubleshooting.
If you have different brand than shown above, then open following link to identify manufacturer's website:http://waterheatertimer.org/Water-heater-manufacturers.html
Add a comment if you need help finding information
10) Post question on professional water heater forum for more eyes on same question:http://www.thetankatwaterheaterrescue.com/forums/forum3/
Add a comment for more free help.
Also take advantage of fixya phone service.
For a price, expert speaks with you over phone while you work on water heater or any do-it-yourself project.
Fixya is always less expensive than a service call.