To expand on what zergesys has said, same sockets doesn't mean equal support. So long as there is support for the new processor on the motherboard side, then great. As you already stated with a BIOS, it is very possible you will need to flash your bios to be able to handle a new processor (and that is only if the motherboard can handle the processor at all).
For a BIOS update, all you will have to do is go to compaqs website and look under their support page for whatever model laptop you have. Buried with the drivers and other downloadable stuff should be any bios updates. Not all laptop models will have support pages like this though, depending on how cheap your laptop is (cheaper usually means less support available). You can also do a google search like "*insert laptop make and model here* bios update"