It's a very long time since I last had a PAYG phone, so I'm just going by what people have posted on these boards, in the time I've been here.
I do know you have to top-up to activate a new SIM.
What I don't know is the error message you would get if you don't, but limited service sounds right to me, as you should be able to make emergency calls or contact o2.
You may want to wait for other poster to confirm what I've just said before you part with your cash.
However, if your phone has been unlocked properly and you have a brand new SIM, I can't see any other reason for the "limited service" message.
SV
Handset: Samsung Galaxy S 8GB, Android 2.3.3
Tablet: Google Nexus 7, Android 4.1