Just tried changing the battery in my wife's Samsung S5 - very simple to swap - but the new one won't charge at all, won't...

My best guesses would be: A problem with the distributor cap or HT leads - since the spark plugs have been recently changed they could have been damaged if they were quite old and "ready to go" when they were moved. -or- A problem with fuel delivery eg. a simple part like a fuel pump/filter, or in a car that age it could be a carburettor problem. I used to have a 1990 Toyota and a carburettor problem eventually killed it off, but if I had my time again I'd spend longer investigating if it could be fixed.