Honeywell HZ-338 Digital Oscillating Ceramic Heater isn't working. I'll turn it on, then the screen and light show for a second, then it turns back off. Can I reset it? How do i fix this?

SOURCE: Similar model compact heater will not "power up" after storage

they is no reset internal the electronic circuit is deferctive some electronics parts need no be changed. i have fixed one and modify it to be more reliable.

SOURCE: honeywell hz-341-bl ceramic heater

take a heat gun or a blow dryer and preheat thermostat and any conductive leads.
after a few pre-heats it will get the idea!

SOURCE: Honeywell Compact Quick Heat Ceramic heater with tilt feature - HZ 325

Your prob is their is a thermostatic solinode that is trigger the unit to go off--because it thinks itself as too hot and unsafe to be on--this trigger was defective or damaged by disuse and/or fatigue------give it a shake-- better yet, when cool and unplugged-vacuum or blow out with compressed air-with out disturbing integrity of workmanship on device--if that no worky--time for new one---thermostatic element is dirty, device being of differing Mghz than outlet, if fairly new device--amperage of outlet is too small for device to work properly. If it is a 240 volt or a 120 volt device and your attempiting to use the wrong voltage outlet--STOP USING THE DEVICE

SOURCE: Instruction Manual for HZ-705

maybe can help

SOURCE: I broke one of he plastic casters on my Honeywell HZ 705

Some full service hardware stores sell replacement casters, you'll just have to find one that will work. Good Luck!