OK, I figured out the problem, with the help of a friend. I put the car in reverse and he listened for the rattle sound. I had thought the sound was coming from the engine, but it turns out it was coming from directly underneath the center of the car around the front seat area / center console section.
Turns out the strange rattle noise was the Heat Shield rattling around after it rusted out. Two bolts where no longer holding the Heat Shield in place, so it was rattling around. Luckily, it was easy to fix, without having to put the car on a lift or jack stands. We just used a 10mm Socket Wrench to unscrew the bolt washer, and just added a larger Washer to both of the two bolts, so that surface area was now large enough to hold up the rusted out section of the Heat Shield. We cleaned up the bolt and hole that it screws into with some WD40.
After tighten the bolts down with the larger washer, it fixed the problem and my car is no longer making the rattling noise. Keep in mind, don't touch the heat shield if you have had the car running. Make sure it cools down before touching it.
It helped having a friend diagnose the problem, while the car was in Reverse. If you are alone, while the car is turned off, you can take a look underneath the car to see if the Heat Shield has come loose . On my 2005 Honda Accord, the Heat Shield is underneath the car in the center console area of the car. Hope that helps