[JD4430]

Hi-Lo-R on the left stick and 4 speed on the other stick.

Range 1,2 and r is on the left. Gears 1-4 on right. If you have hi-lo it is on the dash left of steering wheel. You either have 8 or 16 speeds pending whether you have hi-lo option.
On the left of steering wheel you have 3 options. No lever you have 8 speeds. Hi-lo you have 16 speeds or you have a reverser allowing you to change direction with no clutch

 

[JD4430]

That is a nice setup. My first thought was why didn't the person who installed the backhoe take a couple minutes to remove the 3pt arms. Obvious that backhoe is not coming off on a regular basis.

So everything works. That is good. You didn't check the hydraulic oil dipstick before running it and assuming it is low by the way functions acted? May or may not be true. Being the pump is new you would have to wonder if that really was the issue. Sounds like tractor needs to be gone thoroughly so you are familiar with it including a drain and refill of fluids and filters and a cleaning of the hydraulic screen. The only oil I recommend for that tractor would JD Hydraulic oil.

Check your Hydraulic oil and you will want to plug a gauge into the SCV (where backhoe plugs into tractor) and check pressure using a 2500 psi gauge min. Others here will confirm pressure which I should have memorized by now.

Do you know why the pump was replaced? I would get as much back information as possible because I'm thinking there could be a lot going on here with issues.

 

[JD4430]

Another thought. Which hydraulic functions jumpy? If the backhoe it could be the backhoe is meant for open center hydraulic system where as that tractor is closed.