PSN is free and there is no charge for firmware updates so think you may have your wires crossed.
The best way to narrow down the problem is to connect the PS3 with a suitable LAN / Network cable and see if the console freezes - if it dsoesnt then I suspect you have issues with the wireless signal.
If this doesnt cure the problem then the two most likely causes are overheating (blocked vents ??) or a failing Hard Disk.
Make sure the console has unobstructed airflow (fan is on the bottom) and that there is a gap underneath - if you have a dusty enviroment an air duster would be useful to blow dust out of the fan.
Hard drive is harder to test - although they are laptop drives the PS3 HDD cannot be read by a PC so plugging it into your PC is a no go.