Ha-ha!! News update:
Yeah, work has caught up with me. So much stuff has gone down, it's hard to believe I've been without my system for over a month!!
For Solocon Deus, and anyone else that might be interested:

After my last post, I gave it a few more test runs. A week into it, the mini starts turning itself off and on to the point it refuses to come on. At all.
Needless to say, I freaked out, and made plans to buy a new mini.
Hey, with SuperDrive, faster processor, and I can still use the same HD, $600 was well worth it, right? I bought my car new, it deserves a new unit, right?!
Two days after I bought, I was convinced my original mini did not die. I reapplied the same steps as I did before (which in essence, was disassemble everything, right down to the logic board, and dilute the board in rubbing alcohol). This alcohol by the way is your typical rubbing alcohol that you'd find in a Duane Reade, or a Publix or a Walgreens or something of that nature. I was about to put it all together again, when I realized I might have missed something:
The bottom of the mac mini. You know, the part that logic board rests on. It was still dirty.
And on top of that, the thermal pad looked a bit on the dirty side; and rightfully so, because the soda should have hit there first before it hit the logic board!! I thought that might explain the involuntary powering that led to my initial test's failure, so I removed the pad, cleaned the bottom housing and, applied some Arctic Silver 5 on the CPU.
A reassembly and a few prayers later, I turned it on. No luck.
Went to work and came back. I turned it on. No luck.
I unplugged everything. Went to work the next day. My brother, who didn't know of the prior attempts, plugged it back in, and left it plugged in until I arrived. When I walked in, I noticed the mini was on!! "I didn't touch it since I plugged it in," he told me.
We left it alone.
The same symptoms it showed before it finally powered off are the symptoms it showed before coming on for good! Now, after a week of tests, the mini powers on again!!

Of course, this left me with two minis, and a brand new problem: the regulator on the Car Regulator is fused. But hey, milestone by milestone, all will be up and running once again!

So remember folks, if the spill starts at the bottom of the mini, clean out the bottom housing and replace the thermal pad, as well as clean the logic board. Thanks to all who have contributed, and hope this helps someone!!!