I agree with others: First I'd contact the company for an absolute answer instead of guessing; there's an email address on that label! They WANT to help you, they WANT you to like/use their product, if not sell you an AC adapter.
Secondly, it looks like the center pin is positive. You can confirm that with an ohmmeter as the long, silver, solder strip/path on the edge of the board is most likely (99%) negative.
I like @Tom Carpenter's IC identification. But if all else fails, you can start by applying 5 volts (as with a variable power supply) and looking for signs of life. If not, then 5.5... Then 6.0... Then 6.5...
Determine the higher of the two voltage values on those blue capacitors; write it down. Then note the maximum value of the IC's input; write it down. I wouldn't go beyond the larger valuelowest of what those blue capacitors state on their sideswritten values.