The voltages are okay.
Buying another Arduino board is good, in case this one is damaged.
You can use it to (re)program the bootloader or use it to upload a sketch via the ISCP header.
I use an USBasp programmer myself (with an adapter from 10-pin to 6-pin header).
If the voltages are okay, and everything else is wrong, perhaps the microcontrollers are broken. But in many cases they still can be repaired.
If you have not the official Arduino Uno, but a cheap version from Ebay, the 16MHz could be a very cheap one and get easily broken.
For now, that phone charger is okay.
I use a switching adapter of 7.5V most of the time.