Are you failure with using an electrical multimeter?
The reason I ask is because you can diagnose whether or not your safeties have opened.
Since your furnace does come on for 10 minutes, I believe your problem may be your high temperature limit. I have included a picture of what it looks like.
Another thing to consider is why your limit could be opening. This could be because of a bad switch, a dirty filter, or from the indoor fan not coming on.
The picture of the switch that I have posted is not a carrier product, so yours may look a little different.
The good thing about a Carrier is that they usually have an LED light that blinks to indicate a failure. The failure code is typically printed on the inside of one of your units panels.
Please respond with what you would like to do and I will see it through to the end for you.
HVAC Technician
EPA issued refrigeration license, College certificate, and 7 years in field.