DX6490 won't work on battery only
I presume the camera is out of warranty?
There are many possible problems..
would the old battery charge on the fast charger at all or did it do strange things (dont do it now to try), If the battery was shorted, and you tried to charge it on the dock it may have damaged the cameras internal power supply, which is quite a complicated device, there are fuses but they are absolutely tiny and you need special equipment to fit them properly.
Also the flash capacitor lives on the power board which can keep its charge for quite some time at up to 300v at a substantial current and will make you drop the camera (at least) if it bites you.. :) so from the safety angle if you don't have at least some electronic training I cant recommend opening the camera..
The only possible suggestion that is a relitively easy fix is that the battery contacts may be bent or dirty.
Beyond that as I currently don't have my test dx6490 (used for checking voltages with units in for repair etc..) .. the next try is the dc socket, it may be damaged, or contaminated. try inserting and removing quite a few times and maybe using a VERY small amount of electrical switch cleaner.
Unfortunately to get to the socket if it is broken requires the whole camera be striped down as its just about the first board you fit when re assembling.
If you are adventurous, probably the easiest route to getting a camera back up would be to buy a faulty one from ebay. One with a broken screen or mode switch would be the easiest fix as you only need to remove the back and disconect and reconnect three ribbon cables.
Next would be a lens swap for one with a broken lens but requires quite a significant amount more work.
although the most difficult bit in both procedures is getting the diopter knob (eyepiece focus) on and off which in most cases means a small amount of damage will be done to the eye piece but nothing really bad, just cosmetic (kodak would replace the bit)...
If i can be any more help drop me a line....
best of luck