Remote Key No Longer Working For 2008 Focus

Hi,

I've had my second hand Focus for a few months and a week or so ago the remote key fob stopped unlocking the car properly. I assumed it was the battery, so after waiting for an eBay replacement to arrive I opened the key, put the battery in and gave it a test, nothing. After a spot of googling I found out about the reprogramming mode done via the ignition, I did it and pressed the lock button after the beep, and nothing. I've seen conflicting literature regarding reprogramming the key and if a second remote key (which I do not have) is involved, my own manual doesn't seem too clear on it and numerous forum posts have not helped either.

I don't have a multimeter, so I'm unable to tell if the key is completely broken and needs replacing or if it's working and it's somehow the car that's failing to receive the key's signal.

So, first question, is there any way I can be sure which is at fault, the key or the car?

Second question, assuming the key is in need of replacing, what is the actual procedure? It seems I need a new blank remote key (eBay I'm guessing), that may or may not need exclusive reprogramming by Ford.

Many thanks for any help.