Help pulling information from webserver

Ok this maybe hard to explain but I am currently tasked into somehow pulling data from a Monitoring hardware that has the ability to be put into a webmode and accessed via a local web browser.The device measures various parameters like Temperature, Pressure, Levels, etc etc.

It is able to be set to an IP address but the parameters are only available when physically pressing buttons to get to a WEB MODE.

What I am asking is, what would be a good way to remotely access the information stored on the internal storage. I have tried to SSH into the device and recieved connection failures. This is really hard to explain I know so I will enclose some pictures of what I am talking about