If the blue dots stop spinning on your PS2 and just stay in one solid ball then that usually means that the Clock battery in the system has died and will need to be replaced, on the fat models (SCPH-10000/30000/50000) It is usually located on a little board mouted to the left side of the DVD drive if it isn’t thn it will be located on the main board and will require further disassembly, just pop it out and replace with a CR2032 battery with the flat side facing outwards (writing towards you) on the slim models (SCPH-70000-90000) it is slightly different the battery is located in a little dip infront of the DVD assembly and has a little wire plugged in to the console, replace with the same one of if you can’t find one and are handy with a soldering iron (or someone you know) then get a normal CR2032 Coin cell and there are plenty of guides on YouTube showing how to do it. Note once you replace the battery the Date, Time and other things will have to be reconfigured in the system settings.
Liam H.