HomeGroup wifi v direct cable issue ... SOLVED
Likewise spent 2 days struggling. Both computers LT and DT wired with internet connections and HomeGroup working fine through a Thomson TG585 v8 router. But using wifi connection only, the LT computer would not show for Homegroup use . Much advice tried including MS Troubleshooters, deleting/reinstalling Network and HomeGroup data etc.etc
Finally closed everything down and unplugged all cables from modem.
On restart everything was working perfectly.