Help please...iphone5 when trying to make a call, after hitting green button to make call, screen goes straight back to keypad and all incoming calls go straight to voicemail, any ideas please? Everything else seems ok. No problem with sim or carrier

Hi...I have just obtained a secondhand iphone 5. I'm not technically minded and I don't understand 'geek speak' so please be gentle. I have done all I can think of to bottom this problem. I have switched on and off. Tried different o2 sims (including 2 brand new) that I know are fine, restored to factory settings, changed carrier from 'Auto' to O2 and spent ages on line with o2 chat but everything at their end is absolutely fine. Everything on the phone seems to be working apart from the phone aspect of things. All incoming calls go straight to voicemail and show on the phone as 'Cancelled calls' and when dialling out, I can key in the numbers and get the keypad tone (not dialling tone) but as soon as I press the green key to make the call, all that happens is the keypad pops back up onto the screen. The phone was bought on ebay as an o2 phone (the photo showed Giffgaff on the phone's screen but I understand this to be one and the same?) and as being 6 months old but I have put the serial number into the support website and...surprise surprise..,it must be at least twice that age as the warranty has expired. I have made 2 attempts to have a web chat with Apple Support, have reached the 'You're all set, we'll be with you in 2 mins' and have been left hanging there for over an hour on each occasion, so I've given that up as a bad job!! Any help will be much appreciated...and also, will Apple charge me £25 for each of the aborted chat attempts, please? Over to you...hopefully and many thanks in anticipation.