My camera suddenly would not charge a new battery, and eventually will not even turn on at all. No lights or any other type of response. Camera is Everio mg 77 u.

Your camera can work with 2 AA sized batteries.
Always charge NiMH batteries before using them for the first time, or if they have not been used for a long period.
Always charge sets of batteries together.
Do not use alkaline batteries unless it is absolutely necessary. In most cases, alkaline batteries may have a shorter service life than NiMH. Alkaline battery performance is limited, especially at low temperatures. The use of NiMH batteries is recommended.
AA manganese (Zinc-Carbon) batteries and NiCd rechargeable batteries cannot be used with this camera.
If you are sure you have good batteries, also check if all contacts are clean and shiny. No oxidation is allowed. To clean contacts never use sharp tools. They can damage the camera forever.
Eventually clean contacts with a cotton swap or a dry cloth.
Also check if no debris is in the battery compartment. Just a little pice of paper can spoil all the (camera) fun.
Just to make sure, try some other batteries, then the ones you are sure of, they are fully charged. Perhaps, next time you are less convinced.

The manual says:
The camera turns off immediately even when battery power is full.
The remaining battery power is low even if new batteries are inserted.
•The remaining battery power may not be displayed accurately, and the camera may suddenly stop working, when the type of battery and the settings on [BATTERY TYPE] are not identical. However this is not a malfunction. Depending on the battery
brand and the operating temperature, or if exhausted batteries are used, the remaining battery power may not be displayed accurately.
and:
Use sufficiently charged batteries when using Ni-MH batteries.
You also should set the correct battery type in the setup menu. So put in alkaline / NiMH or oxyride. According to what you are using.
Before you panic, buy a set of alkaline batteries, to make sure your camera is ok. Perhaps you are using rechagable batteries who are not ok anymore.

You should notice for the camera battery type for your camera in the manual. For most camera it only support Li batteries or Alkaline batteries. You can see my tips: why camera warn low power for fully charged batteries

Fuse F351 has possibly blown on the board. It is a 2.5A 32v UL type surfacemount fuse which is soldered to the board. The fuse has a coded letter on it for identification. Recomend you find someone who knows electronics to repair

the camera has a CCD image sensor, it's not very power efficient - therefore it would have that kind of response if you're trying alkaline batteries (brand new or not).

Please try lithium batteries AA or CRV3. Or you can also try a fully charged Ni-mh batteries. It works all the time! (unless the camera is really in need of a repair - www.kodak.com/go/itg)

Have you tried another battery?
Even the lithium ions will eventually not hold a re-charge.
If the unit stays on with external power, there is a good possibility that a new battery will solve the issue

I had this problem with my camera after a year. Scratching the battery contact terminal inside the camera fixed it.

I have somewhat of the same problem, I barely have used my camera as well and a new battery didn't fix it.  Oddly though, if I keep turning the camera on and off and taking the battery/memory card back in, pushing random buttons, eventually it turns back on again.  It's definitely not an ideal fix, but at least I can take pictures, albeit frustratingly.  

camera is not not recoginising the battery may there be a battery type mismatch or battery type is not provided correctly in the software of camera

Had the same problem, took a pencil eraser and scrubbed the battery contacts (both on the battery door and down in the camera), blew out the crumbs and all is well! Camera now powers up and works like new.