How do I run nesasm.exe? Everytime I click run whenever it says "Do you want to run this application?" I clicked the run button and it didn't do anything. Please help me.

I havn't used 'nesasm.exe' myself, but it looks like it's a console application, not a GUI application. This means you'll have to run it from a command prompt window. Open a command prompt, then use 'cd' to navigate to the directory where 'nesasm.exe' is located, then type 'nesasm' and see what happens. Most likely, it'll tell you the correct syntax for running 'nesasm' on the command line.

If this works, but you don't understand the message you get fron 'nesasm', maybe you could post the message here and see if anyone can advise further.

Also be aware that Windows XP SP2 removed the ability to run older (16-bit) DOS executables.

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All it says is this:
Nintendo Assembler (v.1) By Charles Doty (cdoty@doitnow.com)
Original program by J. H. Van Ornum, modified by David Michael
NESASM [-a] [-? (For Help)] infile
Now what's wrong with it?

NESASM is an assembler for NES games, and expects you to provide NES source code as an input. Are you sure you're not looking for a NES emulator? Nestopia, Nintendulator, and FCE Ultra are good ones to try.

Where can I find the Source Code for NES Games? Do I just open an NES ROM in a text editor like Notepad or what?

NES roms consist of binary data, so opening one in a text editor will display garbage. It's unlikely that you'll be able to find the source code for commercial NES games, however many homebrew roms (try PDRoms) come with source.