You need
- a MIDI interface to get MIDI messages into and out of the computer
- some way of creating the MIDI messages (usually via playing a keyboard as you record the MIDI data it spits out)
- something to respond to the MIDI messages you record with an actual sound -- a syntheziser, drum machine, whatever
The OMNI does not have a MIDI Interface, but if your Dell's original sound hardware is not disabled, there's probably a MIDI interface there -- it's usually coupled with the game port and you typically need a special MIDI-to-gameport adapter. Otherwise you need to get something. They come in a variety of types, some that use your computer's serial port, some that use the USB port, and others that require a card slot (these are rare now, I think). They range from $50 or so for a simple single-port (1 in, 1 out) interface up to $400 or more for a rack-mounted pro interface with eight separate MIDI ports (8 in, 8 out) and a SMPTE interface for synchronizing to audio and video tape, etc.
The most flexible way of creating MIDI files is to use a MIDI keyboard. You can get one that is just a controller (that is, one that sends off MIDI messages but contains no sounds of its own) or one that has a simple bunch of presets or one that has a great deal of control over its sounds. The latter would be what you craved if you were a keyboardist and you wanted to program the thing six ways to Sunday to create all kinds of interesting original sounds. Usually for making demos of standard stuff (bass/drums/piano and other instruments that sound like real instruments), a simple keyboard with good standard sounds is all you really need.
If you have something like SONAR or Cubase, they come bundled with software synthesizers that you can access through plug-in architectures (DirectX for SONAR, VST for Cubase). So the computer itself can be the sound source too. But note that to do this sucessfully you usually need a fast computer with plenty of RAM, and you'll get fewer tracks because you're spreading the computer's resources around more. Also the soundcard needs to have ASIO (for Cubase) and/or WDM (for SONAR) drivers available for it if you want to be able to play the softsynths in real time without a noticeable lag (though once the MIDI data has been recorded you can play back sequences just fine with an old-fashioned MME driver). The OMNI, as far as I know, supports both WDM and ASIO.
Most consumer soundcards contain some sort of MIDI synth, but these are usually unsastifactory, unless they are like
the Turtle Beach Santa Cruz or Montego or the SoundBlaster Live or Audigy. These cards can load sound sets in addition to or in place of the standard sounds, and there are many really good ones available that can make a huge difference in the quality of your results.
One thing that you might consider is something like M-Audio's Oygen controller. It's a small keyboard and some other buttons and sliders and stuff which you can assign MIDI messages to (like volume messages and patch changes and the like), has a built-in MIDI interface, and connects to your PC with a USB or serial connector.
If you don't have a keyboard, you can create MIDI messages in a variety of ways -- you can enter the notes in one by one, for example, or edit existing ones to have different pitches. But this is really tedious and I think you'll find that some sort of controller keyboard at least is essential. (There might be something that allows your PC keyboard to be used as if it were a simple controller keyboard, but I suspect you'll be left with songs whose notes are all the same volume, since the keys don't sense how hard you hit them, and you'll end up needing to edit the note volumes to make it sound realistic.)
Finally, you mentioned that you think you need "a Rackmount Midi Effects processor." What for? These are usually effects devices -- reverbs, delays, chorusing, flanging, etc. -- that can be controlled at least to come degree by sending MIDI messages to them. For example, you could configure a MIDI footswitch to send a message for the device to switch from effects program #12 ro effects program #27, or perhaps send a series of messages to increase the wet mix of the reverb over a period of time... (these messages can also be recorded and played back with sequencing software). But this is certainly not something you need at all unless you like to change your guitar effects dynamically.