Digicel is an Irish company, just a seller of equipment. If BTL (Belize Telephone Ltd) is not operating, you won't have any service with a regular cell phone. You won't have service anyway unless you are a BTL cell service subscriber. Some people may dispute that but my Cingular phone service got a message from BTL saying "This call cannot be completed because you are not a BTL subscriber." when I tried to use in last week in Belize. You can rent a BTL cellular handset at the airport in Belize City for BZD$10 per day. Then you can buy prepaid Digicel cards but at BZD$3 per minute for international calls, it's not much of a deal. You're better off renting a satellite phone from someone in the US under the present circumstances (BTL problems) if you want to guarantee your ability to make international calls while in Belize or even Belize intra-country long distance calls. Those cost about USD$50 a week and USD$1.75 per minute.
You're way better off using satellite internet where you can find it in Belize for contacting family or whoever while you're there.