Mac not connecting to SpeedStream

[maherG]

I have a speedstream 6500 router at home and i have 2 computers an HP and a Mac.
originally the mac was connected to the router but every few weeks it decides to stop allowing me to access the internet until i repeat network diagnostics for hours.
now it is not working again.
details:
Mac connects properly to Speedstream but cannot access the internet.
Internet is available because i can access it on my HP.
I have full access to Speedstream but not to the internet.
network diagnostics stops at the point where it asks me to restart router
I once tried to the IPV4 or 6 settings on my HP and used a specific DNS address, my HP stopped working but my Mac worked. then i went back to automatic and they were both working. I read that on one of the sites, this could have been a coincidence but im not sure....
help me please

 

[MisterMe]

To be clear, be sure that both computers are setup to acquire their IP addresses via DHCP. You may assign unique permanent IP addresses to each, but there is no advantage to doing that behind your own router. Whatever you do you to one computer, you should to the other. Else you run the risk of conflict.