- no AC voltage at all reach the transformer. Seem to have problem with high voltage part.
That design of UPS uses the same transformer both for the AC inverter, and to provide power for the charging circuit.
Thus, there is a relay which isolates the high voltage side of the transformer from AC mains, because you don't want the UPS to be back-feeding the mains (or giving AC power to itself) during a power outage. For safety reasons, this relay is normally-open and need to be energized to provide AC mains to the transformer.
This is also why there needs to be a working battery in order to power the UPS on from a completely de-energized state. What happens is the microcontroller in the UPS will start up (from battery power), it will sense whether the UPS is connected to AC mains and whether or not the voltage and frequency are within range, then and ONLY then will it energize the relays to provide AC power to the transformer, and allow the charging circuit to work.
Since you have good battery voltage, and presumably proper voltage out of the regulator supplying power to the microcontroller, then either the power button is bad, or the UPS is effectively "brain dead".