I heard about a ransomware virus going around that encrypts only the first 64 kB of a file. If I was infected with this, would it be realistically possible to retrieve my files?
Not really. If the files had a very large common header (64kb or more), you might be in luck, else you're essentially trying to guess 64,000 "characters". Assuming the file used only 64 characters (e.g. it was a Base64 encoded file), for example purposes, that would be 64^64000 possibilities. That's a number with over 100,000 digits in.
Given that guessing a 12 character long password is considered "hard", and that only has 64^12 (4,722,366,482,869,645,213,696 - only 22 digits!) possibilities, you can see the issue. Guessing a 64kb "string" is over 4500 times harder, and that's ignoring that files aren't restricted to 64 characters in reality.
In practice, a lot of file types wouldn't require all the bytes to be guessed, but most file headers are much smaller than 64kb, so there will be quite a lot of unknown data even so.