@MessagesToEarth
There are quite a few different models of that printer it seems. Some do have wireless capability as well. I'll assume the one you have does not have wireless though.
Just 'how' did you 'connect' the printer to the router? Steps taken would help here.
If you just plugged it in, that might not cut it. Did you look in the Printer's LCD and look at the network settings? There could be some mismatch of settings? Does the router show the LAN port has a cable in it?
You might have a h/w problem, either in the printer's Ethernet port, the cable, or even the LAN port on the router?
However, since you stated you have a printout of the IP Address, then that would sort of indicate the printer did connect?
Where on the Router did you look for it? The DHCP server list? Was any name shown for the same IP Address? HP printer names generally start with HP.
As for Windows 10, how were you looking for it? You do need to install the correct HP Printer driver on the PC to see/use the printer. Not clear you did that? I know you can MANUALLY specify the IP Address of the printer during install, had you tried that?
HP also has some utilities that might help here, such as the HP Printer and Scan Doctor. Did you try using that? It too allows you to enter the Printer IP Address if it can't find it.
I'm on W10 as well, and using the CMD NET VIEW I can see my Wireless printer (I renamed it to HP7855 for easy recognition).
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C:\>net view
Server Name Remark
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\\HP7855 Samba 3.0.37
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When you try NET VIEW, does it report an error?
Since the Printer printout gave you the IP Address, try pinging the printer:
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C:\>ping 192.168.0.107
Pinging 192.168.0.107 with 32 bytes of data:
Reply from 192.168.0.107: bytes=32 time<1ms TTL=64
Reply from 192.168.0.107: bytes=32 time<1ms TTL=64
Reply from 192.168.0.107: bytes=32 time<1ms TTL=64
Reply from 192.168.0.107: bytes=32 time<1ms TTL=64
Ping statistics for 192.168.0.107:
Packets: Sent = 4, Received = 4, Lost = 0 (0% loss),
Approximate round trip times in milli-seconds:
Minimum = 0ms, Maximum = 0ms, Average = 0ms
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Does that work?
Lastly, does the router have ACCESS CONTROL on?