You could open it up and look if you like. Or check out mod boot procedures
here and see if your boot procedure matches up with the no solder or the neo 2.2. It depends on how much use it gets. It doesn't take to long for it to kill your laser. You can change chips but it's not easy unless you are a very experienced at soldering. If you find it to be a neo I would sell the whole thing and get a new PS2 with a fresh laser. The best chip around is the messiah 2.