I don't have an ELK yet but I know how to troubleshoot SMTP issues. Here is what you should do since your ELK is the same network as your computers. You should troubleshoot using IP address first rather than fully qualified domain name(FQDN). This way, we are bypassing DNS service to resolve hostnames.
This should be done on your computer
1. First, find out the IP address of the mail server your trying to utilize
2. Assuming you found the IP address, ping the ip and check if there is a ping response
3. Assuming you get a response, it means that the device/equipment/host is alive
4. If you are using Windows, open up an MSDOS prompt. You can do this by clicking Start then Run then type cmd then press OK button. You should get a black window with a drive letter. That's what you call MSDOS prompt
5. Take a look at an example below wherein the SMTP port 25 is not open. But there could be many reasons why it's not responding.
a.) Either you are connecting to a wrong mail server.
b.) Either your ISP has blocked port 25 from internal subscribers
c.) Either your device/computer is not properly configured with the gateway IP address. This is why it cannot reach the ip address
d.) Either the machine is not a real mail server
e.) Either the machine's SMTP service is down
f.) many more
Make sure that your ELK's ip address and subnet matches your computer subnet. You can't just assign an ip address to your ELK. It has to be on the same subnet such as private Class C address.
Like mine, my pc is 192.168.1.100/24. 24 means 24 bits and is equal to 255.255.255.0. Also, my network is on a class C range, 192-223. Since your first 3 octets are 192.168.1 since you are using 24 bits, you should assign other devices in your net with 192.168.1.x and a subnet mask of 255.255.255.0 also. You can replace x there with anything that is available from 1 to 254. And laslty, verify that the gateway that you set on the ELK is the same as the one set on your computer.
I forgot one last thing, make sure you're using a correct network cable. I don't know if ELK ethernet module requires a cross over cable as I haven't read the manual yet. If you need to make one just cross pins 1-3 and 2-6 pins.
I'm interested in your troubleshooting as I will be doing this in the near future. Please let us know how it goes.
Thanks.