It is probably time to buy a new camera battery. Or it could be your charger. Can you try a known good battery?
I don't think the "keep alive" battery is replacable on this model. Maybe it is but I don't think so. At any rate if it were dead it would not prevent the camera from turning on.
Even a bad internal "time/date" battery should not prevent the camera from working off the main/removable/rechargeable battery. (Date and time just need to be reset each and every time the camera is turned on... Tho it probably can be used without setting them, in which case the info in images would be wrong.)
The cameras that have a non-replaceable "date/time" battery seem to use one that gets recharged by the main battery each time it's used.
As you have already been advised, most likely you just need a new main battery, though a failing charger is another possibility.
However, has the camera been sitting a long time unused? I have seen batteries go so dead, that you need to run them through a half dozen or more charge/discharge cycles before they come back up to full power. First time charged, the camera might not come on at all or might turn off in seconds. 2nd or later charges each power up the camera a little longer, until finally it works more normally. I don't use the LP-E5 batteries, so am not sure if they do this the way some other batteries do.
Camera's die for other reasons, too. It would be great if you could borrow a known-good LP-E5 battery from a friend to try, before going out and buying new.
07/31/2023: New firmware updates are available.
05/31/2023: New firmware updates are available.
05/18/2023: New firmware updates are available.
04/20/2023: New firmware version 1.4.1 is available for EOS R3
03/30/2023: New firmware updates are available.
2/07/2023: New product announcements!EOS R8 EOS R50RF-S55-210mm F5-7.1 IS STMRF24-50mm F4.5-6.3 IS STMRF15-30mm F4.5-6.3 IS STM