HF 400 watt is most likely an MSW... You have just about the minimum amount of battery for that size inverter (you need 200 amp horus per kilowatt you have 0.4 KW or 80 amp hours, A Group 27 is about 90 amp hours)
But there is a long, long, list of things that do not like MSW inverters, this includes a lot of electronics and some motors.
The last entery on the list is "Anyhthing needing too much power"
If you get a TRUE SINE inverter.. Then the list is much shorter,, In fact it has but one entry "ANything needing too much power"
Also, starting requirements can be many times operating power requirements
Though I'd think 400 Watts SHOULD run a fan
Finally,, how is the inverter connected... Plug in or hard wired. (12 volt side, 120 volt side does not matter)
hard wired much, much, much better Plug in only good for about 100 watts if that. If you can (if the power leads are such you can upgrade them) I would use 4GA starter cable, 3 pieces, and a fuse (one holder and fuse) 50 amps or so, to hook direct to the batteries.