I keep having to correct this. If the SIM says Emergency Calls Only, or Limited Service. Do NOT top it up without talking to O2. Normally, when you get a Pay as You Go SIM, the phone will show the network and you will have a signal; you will even be able to receive texts and call the top-up line. But you will not be able to send texts (other than to O2 ) or make/receive calls until you top-up.
I'm sorry, I realise that my previous post sounded a little harsh. I didn't mean it that way. It's one of those things that gets mentioned often even though its untrue. In fact if the number that was associated to the SIM (that isn't connected or has expired) has been 're-allocated' then topping it up would mean you lost the top-up. But someone else would benefit!