Batteries left inside

Really need to know what equipment you're having trouble with. Provide make and model and info on power source (battery, DC power supply...)
In general though, if you can sample your input voltage near the unit with it still plugged in (use pointed probes or skin back wire insulation) and see what the voltage is with the unit turned on. If it drops when you turn it on, look for a bad connection in the line going to the source.

A search of the Fujifilm website provided no answers. Try cleaning the battery contacts in the camera first with a pencil eraser and then with a cotton swab lightly dampened with rubbing alcohol. Also, I would switch to 3 or 4 sets of rechargeable batteries. That way, you always have a fresh set ready and you'll save money in the long run.

GET A MANUAL AND LOOK IT UP YOURSELF

You didn't mention whether you're using rechargeable batteries or throw-aways. If rechargeable, I recommend Ni-MH over other battery types. They hold a good charge, and can be recharged about 300 times. Your short battery life may also be due to corrosion on the battery contacts inside the camera which can prevent full power from flowing to or from the batteries. Try this free fix before you do anything else: remove the batteries and wipe the camera contacts firmly with a dry cloth (heavy corrosion may require cleaning with a wire brush, steel wool, or sandpaper). Remove any residue that may have fallen into the battery compartment during cleaning, then wipe both ends of the batteries and place them back in the camera. This cleaning clears the problem about 90% of the time. If it doesn't work for you, the camera may have a problem that requires professional repair.

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Your camera takes three AAA batteries. For rechargeable batteries, choose NiMH type batteries. When you replace them, make sure that you remove any corrosion that may have built up on the battery contacts inside the camera. Wipe the contacts firmly with a dry cloth (heavy corrosion may require cleaning with a wire brush, steel wool, or sandpaper). Remove any residue that may have fallen into the battery compartment during cleaning,

If this response helped, please post a rating for me. A rating of "Very Helpful" would be appreciated . . .

Your problem may be due to corrosion on the battery contacts inside the camera which can prevent the full power of the batteries from flowing into the camera. Try this free fix before you do anything else: remove the batteries and wipe the camera contacts firmly with a dry cloth (heavy corrosion may require cleaning with a wire brush, steel wool, or sandpaper). Remove any residue that may have fallen into the battery compartment during cleaning, then wipe both ends of the batteries and place them back in the camera. This cleaning clears the problem about 90% of the time. If it doesn't work for you, your camera may have a problem that requires professional repair.

try rechargeble batteries. i switch to rechargeble batteries and they last much longer than regular batteries.

My Dad (in-law) has one of these cameras and has tried several re-chargeable batteries.
Some of the less powerfull ones wouldn't even start the camera, others just didn't last.
He has now resolved to only using Duracell, as they are the only ones which give enough power and he always carries spares.
hope the helps !
OBC

What helped my camra to get working is to make sure you have the right battery.
the kodak easyshare takes only AA/lithium,AA/ni-mi,kaa2hr,AA/zr6 and AA/lr6 and akline too. It does not work for durecell batteries.Hope I helped!

It sounds like a short in the circuit board. Not worth getting fixed unless you find a local person. but first try puting a set of lithium batteries in. sometimes those last forever even when other batteries last less than 10 shots.
other wise try takeing the batteries out whenever you are done and see how long they last that way. then you will know if it is a short if they last a long time.

Hope That Helps,
Caleb