If you have a server ALWAYS use DHCP with it. NEVER use DHCP from the router and NEVER, EVER have them both on. I am very sure it was your firewall.
Just a note. This is not enabled by default. You will have to add the role in Essentials. I can't remember who, but someone PM'ed me about their network not working when they disabled the DHCP server on their router. It's confusing because in Standard, the DHCP role is auto-configured. In Essentials, you have to add it.
Essentials does not have this role installed by default. You can enable it. Check part 5 of the series. Just don't forget to disable the one on your router as Bert indicated earlier.
I've got the basics down now -- over the weekend I figured out lots of things that you have probably forgotten you didn't know. Simple things, like logging into the domain, logging out and logging into the local machine. Honestly, there is no simple explanation of how that works. And you are right, there wouldn't really be any reason for me to use the same laptop on a domain and a workgroup, except in this situation where what I usually do is on the workgroup, and I am testing a domain setup for possible future use, and might want to use the same machine to go back and forth. But I have figured out how to do it if I have to.
The firewall was part of the problem, but so was the router. It was an old one that was in a cupboard at the office, and I brought it home to use for my test setup. I forgot that it was configured with DHCP turned off, and now that you explain that Essentials doesn't have DHCP enabled, I understand why that was also part of the problem.
I will go through your videos again, Sandeep. There are lots of little things to think about before I jump into this-- not so much because I am afraid of wasting money, but so I don't screw up what is already working well, for the promise of working better. I am a lot more comfortable moving this way after this weekend's exercises.