If the pellet stove in our rental broke down a week ago and it hasn’t even been looked at yet, can we withhold rent for the time that it isn’t fixed?

In a case such as this, you can possibly proceed under 2 different legal theories.

The first is known "constructive eviction". If the heat situation in your unit is such that it is driving you to the point of moving out, you may have a legal claim for any costs you incur (e.g. hotel; extra travel time; storing belongings; as well as any attorney's fees that you may incur as a result). You might also be entitled to other remedies, depending upon applicable state law. Any photos and other documentation that you may have (e.g. health department inspection) will add to the strength of your claim.  

The second theory as to do with a breach of the "warranty of habitability". Essentially, this is a guarantee that is implied in every residential lease. It provides that a tenant be given both a safe and sanitary premises in which to live. For this breach you have several options: you can possibly terminate your lease; withhold rent until the repair is made; or make the repair yourself and the deduct the cost from your rent. A lack of heat would qualify as such a breach. As with the first option, this too will require proof for your claim to prevail.

At this stage, you should consult directly with an attorney who specializes in landlord-tenant matters, or at least speak with a tenants right advocacy group in your area. If you attempt any of the above remedies you must be certain of your legal rights under specific state statute.