I bought and installed windows 7 on my laptop and it was activated.. The laptop broke when I dropped it (hardware failure) and I'm wondering if I can use the same windows 7 license on my other laptop?
Any retail Win7 license can migrate to another machine, as long as it is only one machine at a time.
The exception is Builder's OEM, which is locked to hardware as soon as installed, but I doubt you have that on a laptop. If you did, there are sometimes exceptions made to allow it to migrate once such as saying you put it on the wrong computer (in your sleep?).
Just Custom Install, wait until after install to insert key, then activate. At most, you'll have to do a quick robo call to swap numbers which assures it is deactivated on the old machine and activates the new one.
You can still get the cleanest possible install with an Upgrade: booting from the DVD and choosing Custom install to use Advanced drive tools to format before install. The DVD will scan the HD and see the previous OS before formatting it to allow the key, or do the workaround above.