Replacing the Power Supply

The power supply in my HP Pavilion 6535 died yesterday. It was an ATX100. I have an extra case with an ATX 250W power supply in it. I have been wanting to switch cases due to upgrade restrictions in the current HP case(it’s very small)I am concernedhowever, that the motherboard (Intel Celeron 466 Chipset 810)is proprietary with HP and their cases. Also, will the increased wattage in the new power supply be compatible with the processor?