As bhai said, it means the writer doesn't have access to a computer at that moment. It doesn't mean he doesn't own or use a computer, simply that he is not close to/near/by a computer so it's not possible for him to use one at the time of writing/saying the comment.
Not "by a computer" would mean not in the proximity of a computer, but not that the person does not have access to one. To not have access could simply be that, while the computer is nearby, someone is presently using the only one available.