There are serious misunderstandings in the statement you quote. The central one is that breaking cryptography is about brute force. This is in fact a mostly irrelevant threat for many modern cryptographic methods, and especially for encryption. Cryptography tends to be significantly overengineered against brute force.
I'd setup a computer or if I'm really curious multiple computers to brute force using the AES algorithm. It'll probably take a while but I know for a fact that after a finite amount of time, I'd decrypt the drive.
This statement is technically correct except for one word: I'd decrypt the drive. No, you won't. You'll be dead long before that. Let's say you are one of the most powerful entities on earth and you devote as much power as the whole bitcoin mining infrastructure to breaking this encryption. Bitcoin manages about $2^{67}$ hashes per second by consuming about 5% of the world's total electricity production. The cost of trying out an AES key is comparable to a hash. Let's further say you'll be happy with a $1/2^7$ chance of success (almost 1%), so you'll need time to try about $1/2^7$ of the $2^{128}$ possible keys. This will take $2^{128} / 2^7 / 2^{67} = 2^{54} \:\mathrm{s} \approx 6 \cdot 10^8 \:\mathrm{yr}$. That's over half a billion years. That is such a long while that in practical terms, it means it won't happen.
Electronic computers make the gap between the attacker and the defender so huge that the attacker has absolutely no chance with a brute force attack. Attacks on cryptography come from other fronts: design mistakes, implementation mistakes, or insufficient protection of keys and other confidential material.
How much harder would that be to brute force?
About the same, but as we've seen, this question is irrelevant anyway.
I'd have to brute force attack with AES and possibly every other known encryption algorithm.
No, you wouldn't have to brute force. You could find another way to break it, such as a design flaw in the encryption.
So, would that be impossible to decrypt since I have no algorithm to brute force with?
No, it wouldn't be impossible to decrypt. It would just mean that you'd have to find some flaw. Which, once again, is how all encryption is broken. (Any encryption that is vulnerable to brute force has a major design flaw, because it is well-known how to design encryption that's effectively immune to brute-force attacks.)
Designing an encryption mechanism is hard. Schneier's law says that anyone can create an algorithm that they can't break themselves. The difficulty is creating an algorithm that others can't break either. This is difficult even for experts, which is why all serious cryptographic methods are independently reviewed by many experts before anyone puts them into production. Using a well-known, well-respected algorithm is safer than using a home-made one.
