If the flash does not fire under any circumstances, then thats at least part of, if not the entire problem. If you look under the Custom menu you'll see: release when charging..... Off is the default setting, and if its still set like that, it matches the symptoms you are describing.
You can send it in to Pentax for repair...but I suspect the cost of repair will be rather high....considering you can buy a used one for about 200 (or less) these days. Another option is to use an external flash mounted to the hot shoe. The DS uses ttl flash, and nice ones can be found for next to nothing.
Or its a great time to upgrade to k10 or k20
I still have my DS, and love it just for the small size and ttl flash system.
Good luck with whatever path you take....