You never replied to Gerry's question about Device Manager or provided a screenshot. Printers do not normally show in Device Manager, so it's not at all clear what you are seeing.
Type "snipping tool" (without quotes) in the Start > Search box and click the link to open the Snipping Tool. Use this to capture and save an image of Device Manager. Then upload it using the "upload image" icon which is the second icon from the right
in the Reply box's tool bar.
It's not clear what you mean by "installed software." You say that you can print from Notepad. How exactly do you manage that? Please explain step by step.
It's not clear what you mean "does not show just keeps on searching" in response to Ron's question about using the Add printer wizard. What exactly happens when you click the link to start the wizard? Please explain step by step until you get to whatever
point you mean by "keeps on searching."
It's not clear whether Devices and Printers is entirely empty or just that the HP 3050 isn't showing. Are
any devices or printers visible in Devices and Printers?
It's my understanding that the HP Deskjet 3050 can be connected either wirelessly or by USB. From your statement that your printer is "on a network not shared," I assume that it's connected via wifi. Is that to a router/wireless access point or directly
to your computer? In either case, have you used the printer's front panel controls to determine the printer's current IP address and other network settings (including whether the printer reports being connected or not)? If not, please do that and report
your findings.
Assuming that the printer is connected to a wifi router/access point do you have any other devices that are connected via wifi to the same router/access point? If not now, have you ever had any such devices connected?