So you now have a new front washer jet motor installed, ...there is washer fluid in the bottle, ...when you use the washer jet (can hear the motor running) with the pipe off where you fitted the new non return valve does washer fluid come out there?
If so then I'd say that a pipe is off somewhere between that & the windscreen wiper arms.
There are something like 6 washer jets on each of the front windscreen wiper arms/blades so doubtful they are all blocked so I'd be checking all the pipe work leading up to them making sure it's all connected & not blocked somewhere.
Also are you positive that the new non return valve you've just fitted is in the correct way around?
If it is the wrong way around it will not allow water to pass, ...usually they have an arrow on them indicating the way water flows through them.