Denton to Manchester Piccadilly: http://traintimes.org.uk/denton/manchester/08:45/saturday -- the train only runs twice a week, on Saturdays.

Although going outside Northern Trains' area does indeed seem to prevent fares being calculated: http://traintimes.org.uk/denton/deal/08:45/2022-10-22

For those of us less familiar with the British rail network: why would Denton to Manchester Piccadilly be a challenge to book a ticket for?

There's no fare set for that pair of stations specifically[0], so no way of buying a ticket. You could get one to Stockport and another from Stockport to Manchester, but that's obviously not quite the 'any station to any other station' mentioned. There may also be some kind of Manchester all-area ticket that's valid, but again that adds a knowledge requirement.

(Denton is mildly famous amongst British rail enthusiasts as it has a 'parliamentary'[1] service of one train a week each way. Useless for actual travel, but (partly because of an unusually pleasant station buffet with good beer at Stalybridge) the regular site of meetups for rail geeks).

[0]: https://www.brfares.com/!!expert?orig=DTN&dest=MAN

[1]: https://en.m.wikipedia.org/wiki/Parliamentary_train