I’m just a coder, not a mathematician or a crypto expert. But there certainly is a class of ciphers and crypto algorithms that are genuinely impossible to break without knowing the key, it’s called “perfect security”.
A one-time pad fits that definition. The Wikipedia link I gave above lists several others. Most of the crypto algorithms that provide perfect security aren’t ciphers as such, but things like secret sharing schemes and key exchanges.
Again, OTP is worse than useless for almost all practical applications, but it does provide a counterexample that disproves the general claim that all ciphers can be broken given enough computing resources.
To explain it using your credit card example, imagine my a + b = c equation with bigger numbers. a is a secret credit card number, b is the key, which is random and has the same number of digits as a, and c is the ciphertext.
If you know c, you could easily generate every possible value of a by running through every possible value of b. But that’s useless - all you’ve done is produce a list of all possible credit card numbers. You’ve learned nothing about which specific card number is contained in my message.
Now, if you have an external source of information about either a or b, the OTP becomes trivially breakable. Likewise if I screw up its implementation, such as by using the same key more than once. It is secure only under very specific assumptions, which is that neither the key nor the plaintext are leaked in any form through any other channels. Which is why they turn out to be virtually useless in practice (and I’d suggest avoiding any crypto product that claims to use a one-time pad - you won’t be able to meet those assumptions, so it is guaranteed to be insecure).
Steering back towards the OP: TrueCrypt and GPG are not perfectly secure by this definition. But they are almost certainly vastly more secure than anything else you have. They are strong crypto products, and the way strong crypto is usually broken is not with mathematics or supercomputers. It’s broken by other means: people make mistakes, leave the passwords lying around, leave the originals lying around, someone installs a keystroke logger to record the password, shoulder surfing, and so on. That’s what you need to worry about, not the mathematical security of TrueCrypt or GPG.