I take it you do not have a DMM (digital or any type of multi meter), which would allow you to diagnose your lack of continuity to the atomizer. If you're going to use mechanical mods, you should invest in and learn how to use a DMM.;-)
Assuming your batteries are in good condition (another thing you could verify if you had a DMM), then diagnostics will be rather short and, in your case, probably not that useful.
Fit a different, "known good" atomizer. If the problem disappears, then you have a atty with a electrical "open" - an open circuit.
If the problem persists... then you are not getting battery voltage to the atomizer... and knowing the issues that can occur with side button mechs, in all likelihood, it is the button itself that is not passing on voltage to the 510 connection.
If I had it in my hand, I could quickly identify and correct the problem, but as I don't... I'm sure you can find some instruction on-line, describing how to disassemble, inspect, clean and reassemble the mech and button assembly.
Am I beating you up a bit for not having a DMM? Yes I am. Mech users, RBA users, rechargeable battery users... all should have a DMM just for the issues you are currently having. Without one, you are electrically blind.
Cheers