I had the same problem when i first activated my account.Internet only worked with data on. What worked for me is i reset my modem...so i unplugged it for ten seconds and then plugged it back in. By the way i have a 5g modem and had no problem connecting to wifi even though my data plan only includes 3g speed. Hope this helps.
This thread is nearly 9 months ago and has not been replied to since then. Either way, Wi-Fi not working isn't related to activating or using Public Mobile services.