You don't say what type of beat valve it has, but your head is not that high.
Firstly reduce the stroke of the beat valve so that there is a greater velocity head across the seat, if this is still not enough, add a light spring to remove part of the weight of the valve until you get it working.
Your 100ft drive pipe is very long and will cause a fair amount of frictional loss so your water velocity may be too low to lift the valve.
If you want the thing to work properly get rid of the plastic drive pipe, the elastic losses in it will stop you from ever getting good results.
Feed your water nearly horizontally to within 20 ft of the ram with a wide bore plastic pipe to a small tank so that the head in the tank is the same as your supply.
Take a steel pipe from this tank about a foot below water level and run this straight to the ram. Make sure all drive pipe joints are perfectly water tight.
The polly pipe is ideal for the delivery.
Make sure the delivery valve seat is sealing, if it is an old valve it may leak back.
You don't say anything about valve sizes or water supply available so I can't advise on the best size of drive pipe.
Try reducing the stroke and adding a bit of a spring to get it running then you can see if the present drive pipe is anywhere near the right size. Don't expect much performance at 40 ft lift with that plastic drive pipe but it should keep running.
Flux