Is it legal for me to hack another one of my own computers?

I'd say 99.9% yes, but can imagine that someone could think of a reason that it might not be... like if you agreed to let someone store confidential info there, or something else odd like that.

What is the situation?

I just want to see if my other computer would detect it. How legal is hacking anyway? Isn't hacking only illegal if you do unauthorized harm to a computer or obtain financial or other personal information?

In legal terms the word hacking is not used, unauthorized access or wire fraud are some of the terms used. It depends on what the action was.

Hacking:
1. Informal. To alter (a computer program): hacked her text editor to read
HTML.
2. To gain access to (a computer file or network) illegally or without
Authorization: hacked the firm's personnel database.

I just want to see if my other computer would detect it. Does the program I would use affect weather or not its legal?

I just want to see if my other computer would detect it. Does the program I would use affect weather or not its legal?What program are you planning to use and where are the two computers?

I'm not sure what program to use yet since I'm not sure if they are legal or not. The two computers are in the same house.

If both machines are owned by yourself, then as NK pointed out this ISN'T hacking and is perfectly legal.
What app you use is completely irrelevant

If you are using Windows then you do not need any external programs to see if the computers can "see" each other over your home network.

But would using external programs be illegal?

Not if you are staying within your private network - you can do whatever you want there.

All right, thanks for the help everyone.

Hacking has many meanings and levels. Generally it refers to gaining access to some hardware and/or software through a means not provided by the makers of the hardware/software.

Hacking, by itself, is not illegal. Gaining unauthorized access to a private computer system is illegal in the US. Don't know about laws outside the US.

Possessing hacking tools is generally not illegal, though some tools are like the ones that permit copying of encrypted DVDs.