Calculate how much time is lost by the delays and crashes caused by old hardware. If you can break down how expensive not upgrading is, it might be easier to sell the upgrade. You could also break down the upgrade into waves, replacing only a third (or maybe a fourth) of the machines each year, starting with the oldest, and with the users who rely on them most. Another benefit to the wave approach is that you’ll reduce the likelihood of having to do another big upgrade every 3-4 years.
This is not the way.