keeping the key safe, yes, using the key once, yes, but need not be random at all (with in reason - a key of 0s is feasible, under the pretense that the cipher text, which would be equal to the plain text, is the cipher text for any message with the same length, for some key)

the key space being the same size as the message space, and cipher text space means that all messages of equal length are possible, with no way of knowing which one is the correct one. i suppose, a theoretical attack would be to be to enumerate all messages in the english language, XOR them with the cipher text, and see which resulting keys come close the properties of the PRNG used..

even non-determinism can't help you here, i'm afraid.