Difficulties connecting desktop(wired) & laptop(wifi) via Homegroup

I am assuming that you can access the interwebs on both machines.

the ping tests you've done, I assume you've starred the last octet out for some reason rather than post them. NB a 192.168.x.x address is private address class, which is just accessible within your LAN and is therefore secure.
the results from the ping looks like it's being blocked by something, Either windows or a third party firewall or your shared wifi router...

how are you getting your IP addresses ? from the IPconfig it's not conclusive, if you add the switch /all to the end of the ipconfig command you will get a bit more information. anyhow, if you've manually entered the IP addresses then maybe the ip address for your desktop machine is already in use on the network....

Nothing, huh? Eighty people looked and said, "Pass!" Not even a "I feel your pain, networking is hard." Did it ever occur to you people that what I really needed... was a little solace?? Well, even if go it alone, I must (did I just channel Yoda?), I figure it might be worth it to chronicle my plight for any other poor schmucks who find themselves in my situation. If anything sounds familiar to anyone else, feel free to weigh in.

It's just as well the SevenCrew is at a loss. I'm becoming more and more convinced this is a network/router issue, anyway. Like I said earlier, my laptop 'sees' my roomie's laptop under network in explorer, but my desktop can't. Also, thinking on the whole wireless vs wired bit, I realized that I have another machine right here I pieced together from spare parts. I once thought I'd use it as a server for me to access files over the internet (I dream of running before I can crawl). The point: I've got it hardlined to the router, and I wandered if my desktop would be able to see another wired machine. Bada-boom, bada-ping, it seems to be able to. However, my laptop spews the same old "Destination host unreachable" line when pinging the Ubuntu machine. So, I guess I'll work this wired vs wireless lead a bit more.

I spent some time with what I'm pretty sure was an automaton on the Belkin tech support chat room. It didn't really get me anywhere, but I was told I'd get a call from tech support today and they'd try and help me out. We'll see.

Lol. Guess Anta was posting while I was still mucking about with my second post. Glad you dropped in. To answer your questions:

I used the stars because I didn't want to type the ping results twice. The results were identical whether pinging desktop -> laptop or laptop -> desktop. I simply meant to represent both at the same time - a bit of concise laziness, if you will.

I have both machines setup with static ip addresses. Well, actually, I gave my laptop one last night - testing it both ways. I've always heard it's good practice. I put them in the 70s to keep multiple machines from using the same one - until 70 of my friends show up with laptops, that is. =D

I'm glad you mentioned the firewalls again, though. I turned Windows firewall back on after giving up for the night, so it's been up during my tinkering today. Might have to go back over some things.

For servers, tis a very good practice to use static. helps with DNS registration and keeps network traffic down..
however for mobile or client devices, I find statics a pain in the 'arris to be fair.
everytime you access a new network you need to change your config manually, let the computer do it !! lol

you didn't answer do both machine access the web ok ? and the problem is only with joining homegroups....

if you've set static for both machines, you may want to have a shufty through both configs again.
a slip on subnet octet and no flicky flicky.
one digit out on the network address and no flicky flicky
using a network address already in use on the network and no flicky flicky...

You know, I hadn't considered the mobility of my laptop when giving it a static ip. That's a damn good point that would surely cause troubles for me on campus (WAY more than 70 friends there.)

Oh, and all machines are able to surf solo as well as they please.

Here's links to my ipconfig/all results for desktop and laptop - now with random IP traveling power!
.....
Actually, you might find these easier to read:
Desktop1/2 Desktop2/2 Laptop1/3 Laptop2/3 Laptop3/3

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.