HomeGroups

I have a laptop with Win 7 using wireless. I upgraded my HP desktop to Win 7. Both have HomeGroups but only 1 shows the name of the homegroup. I can't figure out how to get both these computers on the same homegroup and to recognize each other.

Thanks

Are they both wireless? You can't get a wired to connect with wireless... they lack common language. You need an adaptor.

what kind of adapter? Laptop is wireless thru wireless router, desktop is hardwired to internet

As long as both computers are on the same subnet you should not have an issue.
Perhaps use this walkthrough and see if starting over will help.
Windows 7 HomeGroup: Walkthrough
There is a small caveat which I think should be highlighted in the interest of starting on the right foot

On the first computer, which must be running Windows 7 Home Premium or better

Windows 7 HomeGroup: Walkthrough

Both computers generated their own passwords. I unjoined Homegroups on both PCs and am nowt ready to join on both computers. . A possible problem my be that My desktop PC says in is connected to "INTERNET" My Laptop is connect to a Named internet connection. See 2 Images attached

The snippits you supplied do not seem to agree with your description. If you had already created a Homegroup, the second computer would show "Available to Join", not a "ready to create".

Maybe you should leave the Homegroup on both computers and reboot both systems, then create the Homegroup again on the primary system and try joining from the secondary system.

I left homegroups on both computers. I started the walkthrough from scratch on both computers. Both computers try to create a homegroup. The 1st computer created a homegroup and password. The second computer doesn't start the "Join a Homegroup" Wizard but tried to ran its own "Create a HomeGroup" wizard and generate its own password.

Have you run the Homegroup Troubleshooter?

Also, you might check the Services.msc panel and see if you have the Homegroup Services running,

HomegroupProvider and HomegroupListener

But if you have a Homegroup set up on one system and the other system still shows "ready to create", the second system is probably not seeing the first on the network. And this, of course would depend on the limitation Trouble mentioned about which versions of Windows 7 can create a Homegroup.

both of these say startup type manual mode and it is blank in status field. Do I need to switch these to automatic on both computers and reboot both computers?

You could try just starting both services to see if it makes a difference. Mine both show Manual starts and are currently running, and I do not run Homegroups.