yes the browser works its also a japanese import
What firmware are you on? 3.60, 3.63, 3.65, 3.73, something else? This is important as $ony changed the authentication handshake and doesn't allow lower than current firmware to connect. See this thread for info on that:
https://gbatemp.net/threads/error-np-2239-6.591129/
Basically you need to update to the latest official firmware (3.73) to be able to register/create a psn account for your Vita. However I'm guessing this isn't the likely culprit because you said you started following the guide which starts by having you update to 3.73. So are you on 3.73 or something else?
This issue was affecting the European region servers back in November of last year so it is entirely possible it's come around again. In that instance it was basically a waiting game. Took them almost a week to fix it then so there may be a similar issue happening now...
When you got the Vita had it been factory reset for you? Vita's are weird in that you can only tie one account to them so if it wasn't factory reset you may try that. You can factory reset it by turning the power off and then holding the R, PS, and power buttons to enter safe mode and selecting option number 4 "restore ps Vita".