I had the reverse situation as an American traveling to Iceland when no chip+pin cards were available to me. I picked up the rental car with an almost empty tank. They point me around the corner--the gas station is automated. I start driving the 50km to reykjavik and cross my fingers.
Later in the trip I get into a similar situation of an automated gas station in a desolate area. I waited until a local came by, offered them cash to use their credit card. They seemed suspicious like it was some sort of scam (I dont blame them), but thankfully that worked out.
I was stuck. I eventually found a shop inside that would sell me a bus ticket if I bought something else.
10101 and 01010 are also valid zip codes.
(00000 usually works too even though it's not a valid zip code)
Here's an arbitrary one I know exists: 85310. Try it next time and see if it works.