Did they say what type of painkiller they had given him? The medication chart should be kept by the bed and this should record all medications and frequency. I know that's no good to you at the moment but have a look next time you visit. If the pain killers are noted on the medication chart for regular prescription then the nurses can administer these - they don't have to be dispensed by a doctor.
With regards doctor coverage at weekends, when my Mum was in hospital there was no doctor coverage at all on the elderly wards during the weekend. In case of emergency the nursing staff had to ring for the 'on-call' doctors - they took over an hour to arrive when called. I heard recently though that the nurses told the family of someone in severe pain that there were no doctors at all available and they would have to wait until Monday to get any pain relief! It's unacceptable, but at least your father's ward has one doctor available, although as you have found trying to get hold of them via phone is practically impossible. The ward sister or head nurse should be able to tell you if pain relief is being given, what type and how regularly though - you don't need to specifically speak to the doctor if the staff have already confirmed that your father is on pain relief (providing they are telling the truth!) .
I have found that trying to get effective pain relief in hospital for someone with dementia can be very difficult as the staff don't always identify when someone is in pain, or listen to family when they say that the person is in pain. The important thing if your father is in pain is that they give him suitable pain relief, establish the cause and carefully monitor him. I hope you manage to speak to someone who can let you know what's happening.
