My time capsule froze. Won't start. If I rest the machine, will I lose all the data that was backed up on the time capsule?
No data is lost by any reset.
If it froze what is the LED doing at the front?
If it has gone off, give us the model of the TC from the rubber foot.. A1xxx
You are likely seeing a dead power supply.
If it is a later model then it is more likely actual hard drive issue which could mean your files are gone.
Important if the front LED is solid amber that can indicate a dead drive.
Leave the TC to cool down for a few hours and then try restarting it.
Unfortunately, either the hard drive has failed, or there is an internal power supply problem with the Time Capsule.
If the Time Capsule is in warranty, take it to an Apple Store near you...if you have one in your area...or contact Apple Support directly. http://www.apple.com/support/contact/
If you have AppleCare in effect, the Time Capsule may be covered under the extended warranty.
If the Time Capsule is not covered, Apple will not offer any type of repair service, but there are options available in this link provided by LaPastenague.
If the TC is out of warranty.. and apple care.. which on any computer will also cover the TC if it is less than 2years between the purchase and the TC is no older than 3years.
You can open up the TC and change the hard disk.. at least disconnect it to find out if it is the problem.