First, assuming that the battery is charging properly, there are two other connection issues that may cause this. An insulating film can build up on the contacts in the battery compartment or one of the contacts can lose tension. Clean the contacts in the battery compartment using q-tips with a small amount of alcohol and clean q-tips to dry the contacts. In addition, check their position in reference to the contacts on the battery.
Also, have you tried completing the setup with the memory card removed? If not, please do so, as checking the read/write function is part of the self check portion of the start up process.
Please keep in mind that my diagnosis & solutions provided are directly dependent on the accuracy of your description of the problem. As with any "do it yourself" fixes, success is a "team effort", since I can't see or touch the camera, and relies on the customer's manual dexterity and ability to follow the instructions well. If the "do it yourself" approach doesn't work out for you and you need conventional repair, please let me know.
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Unfortunately, the fact that the camera is asking for the base settings (language, time & date) indicates that the camera has effectively been reset and is attempting to come up from the original factory status. The symptom does point to a software or hardware issue, but, probably not electrical, since at the next step there would be lens movement and any obstruction can cause the shutdown. Try using canned compressed air to blow out the area between the lens barrel and camera body since even a small amount of sand or grit can cause this problem.