I would say most Valve games can probably run fine in your setup. That said I would probably use your setup more to fry eggs than game on. That system if it had seen no service in all those years will cook like an induction stove in short time with any game that you would try pushing it in more than 40 minutes play. Also I am sure things such as repasting of the CPU/GPU have not been done in all these years, cleaning of fans and most certainly switching out that dreadful HDD for a SSD before it reaches its final knocks of death.
If I were you I would start putting money in a jar for a newer system. Because I can only imagine how much longer that laptop will continue, its basically on borrowed time at this point.