No phone lines = no credit card transactions, no debit card transactions. Some store cash register systems are on computers, so no power no credit/debit purchases.
I have paid in cash for purchases tallied by the cashier with a calculator ( taxes etc…) when the power was out. Many stores will not handle credit card transactions manually (remember the kchick-kchick machines ?) because of widespread fraud.
Cash is best – is my policy. Besides you can’t bribe anyone with a credit/debit card :-))