A couple of years ago I bought my Mum a wireless doorbell for her flat - she live on the first floor and has an external door where her old bell was placed and an internal door at the top of her stairs - the bell itself was on the wall in the living room. The wireless one did not ring when we tested it so she continued with her old one - which is now broken.
Should I try with another wireless one with a longer range (not sure what the range of the other one was) or should I go for a wired one - and if so how difficult is it to install
Wireless bells are very simple to fit and the range is plenty enough for most people. Have you checked the batteries are seated properly and terminals clean in the press end and the receiver?
My father used to have a wireless one where the receiver needed batteries - it was never very good. He replaced it with one where the receiver plugs into a spare electrical socket - this one works perfectly all the time.