New Pressure Switch -- low water pressure
Just because 20/40 was stamped on the original pressure switch doesn't mean the actual cut-in pressure was 20 PSI and cut-out was 40.
Almost all pressure switches can be easily adjusted, a 20/40 model could be adjusted to as high as 60/80, some of them even higher.
If the house and the pressure tank are at about the same elevation, 30 PSI is pretty low pressure. 40 or so would be about the minimum. Try adjusting it up a bit.
If this new switch has an adjustable differential, back it off as far as possible. 10 or 15 PSI of difference is much better, but if you have a small pressure tank, you'll short-cycle the pump, and it won't last very long.
If all this talk about pressure is just a bunch of gibberish, write back. Several of us can explain the actual hows and whys of a water system, and help you dial it in just right.