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.