So based on this old question of mine I figured out that I can reset the access point and access it using telnet through a wired Ethernet connection.
I have set a new password, I have set up the Ethernet connection so it doesn't conflict with my main router, and most importantly I have specified the country because this turns the WIFI radio on - except it didn't...
I have the Getting Started Guide and also the Management and Configuration Guide as well as this official FAQ. They all indicate that the WIFI radio is turned on when I have specified the country.
--> Why does the status still say "Radio Status : Disabled"?
HP ProCurve Access Point 420#show system
System Information
============================================================
Serial Number : TW413QB09X
System Up time : 0 days, 0 hours, 4 minutes, 3 seconds
System Name : Enterprise AP
System Location :
System Contact : Contact
System Country Code : AT - AUSTRIA
MAC Address : 00-0D-9D-F6-65-78
IP Address : 192.168.1.3
Subnet Mask : 255.255.255.0
Default Gateway : 192.168.1.1
VLAN State : DISABLED
Management VLAN ID(AP): 1 (U)
IAPP State : ENABLED
DHCP Client : DISABLED
HTTP Server : ENABLED
HTTP Server Port : 80
HTTPS Server : DISABLED
HTTPS Server Port : 443
Slot Status : 802.11g
Radio Status : Disabled
Software Version : v2.2.5
SSH Server : DISABLED
SSH Server Port : 22
Telnet Server : ENABLED
Max Telnet Session : 4
Serial Port : ENABLED
Reset Button : ENABLED
SSID Number Supported : 8
============================================================
From the FAQ you linked it has to bet set and saved: