750goes has a good methodology for getting you running again. I wrote this while he was posting FYI...
Haven't heard of anyone who got a CB400F to work right with pod filters. They came close, but always at 1/8 to 1/4 the throttle response was poor with a wheeze/ stumble. This seems to indicate a need for a different cutaway ramp for the slides, which is not an easy adjustment. Most either lived with this foible or went back to the stock airbox to get the nice street performance back.
Do check your plugs. If you have changed the main jet and slide needle for a richer mix in order to get a better low throttle response, you could have easily sooted up the plugs so they short out on the carbon deposits instead of jumping the spark gap. New coils won't help carbon fouled plugs. Either clean your plugs or replace them. Spark plugs aren't new unless you just took them out of the box.
Remove one of the plugs and lay them on the engine to see if they spark >>across the gap<<. If so, look elsewhere for your starting problem.
Check your plug cap resistance and your plugs. If you have resistor plugs then replace your caps with non-resistor types.
To improve your low throttle response, turn your Idle Air Bleed screws in (1/8 at a time) to try and compensate for the lackof vacuum the pod filters provide for the carb bores. That is where the carb sucks on the jets. If the vacuum is lacking, less air should be provided by the Idle Air Bleed screws. If the Idle Air Bleed screws are hollow tipped, you may run out of effective adjustment range and then you must get larger slow jets in order to get more fuel into the carb bores at idle, which improves low throttle position pickup.
Hope you have a test track to determine your new Main jet size and slide needle settings. And, learn to read spark plug deposits for combustion conditions under actual loads. The pods or no air filter mean all the factory settings and adjustments are unlikely to be correct.
You are aware that ALL the basic tune up items must be spot on before dialing in the carbs, yes? Also, pretty futile without a carb synch. But, if you like doing the work over several times, then tune the carbs first.
Good luck!