Also, can you tell me what you had to change in the code that I posted?

Most if it was just getting getting the use lines right. This line:

flock DBM, LOCK_EX;
[download]

...originally had LOCK_EX in quotes. Since I always use warnings, it said unto me:

Argument "LOCK_EX" isn't numeric in flock ...
[download]

So how do you suggest I deal with file locking?

Use a separate lock file, and lock it before you tie. I'd be really surprised if there isn't a module to do it for you, but I don't know off the top of my head what it would be.