Connect to a 5V USB 1A wall charger like many phones use for charging and leave it on overnight.
If memory serves me correctly the blue power on button and the A, B, X, Y buttons all flash when first plugged in. Later on only the Power button will be flashing. When fully charged the Power button will glow solid blue.
If the controller has been in storage for a long time it may take 12 hours or more to fully charge.
You can safely assume that. Ran into one a couple years ago like that where the electrolyte leaked and corroded the over charging circuitry on the battery.
Do a search for a lithium ion battery cell of 2.22Wh to use as a replacement. Open the controller, unplug the battery, and carefully peel it off of the double sided tape that secures it to the circuit board.
Measure the length and width and find a like battery using a web search. It took awhile but I was able to find a suitable replacement in stock.