Your description sounds like you're dealing with the difference between speaker-level (amplified) outputs and line-level (unamplified) outputs.

The speakers that you're having to "crank up"... Are those self-powered? (Do they have their own power supply and on/off switch?) You might be plugging the laptop's line-level (unamplified) output into speakers that have no amplification.

Alternative explanation to the laptop situation: Laptops have a separate control for the speaker volume that is not related to the Windows control panel volume levels. Usually you need to have the proper piece of keyboard interface driver software installed (it usually comes with the laptop, but it often gets deinstalled, or forgotten when you reformat the laptop's hard drive), then you need to press a function key combination on the laptop's keyboard to increase and decrease the volume of the soundcard.

The speakers at home that you have to turn way down: I'll bet those are self-powered. The fact that you have to turn them way down might be normal, or, maybe your PC has both a speaker-level (or amplified headphone level) output as well as a line-level output and you've plugged them into the wrong one.