XPS 8700 powers off when coming out of sleep, then starts up a few seconds later. Is this sign of trouble to come?

Ok, so, before this symptom started, I was given a pair of DDR3 RAM sticks, and tried to add them to my system.  I did, but then I would get the 4-beeps error.  I then, via trial and error, sampled them individually and together, and isolated the problem in that one of the new pair of RAM sticks is defective.

Note, each time I was to make any RAM changes, I would unplug the PC, and hit the power button in order to drain any residual charge.

At one point during this trial and error period, I got stuck in a power-on-power-off loop.  I would hit the power switch, and for less than a second, the fans would spin up as if the PC were going to power up, then it would shut down.  After about 2-3 seconds, it would, on its own, attempt to power up again, and in under a second, shut down.  It would do this until I pulled the plug.

I did a bit of online searching and found a suggested solution of:

1. Pull the plug
2. Hold the power button down for 20 seconds
3. Plug back in
4. Power on

This worked.  From that point on, it powered up, and everything seems to be behaving fine, but I haven't tried any hard core gaming or anything that might stress the system yet.  Plenty of web browsing, and YouTube, though.

However, this is where it gets weird.  Normally, when I put the computer in sleep mode (sleep button on the keyboard), the computer would go into sleep mode, with the power button LED turning amber.  If I hit a key on the keyboard, it immediately wakes up, power button LED goes from amber to white, and everything is fine.

Now, however, while hitting the sleep button puts it to sleep as expected, hitting any key on the keyboard to wake it up does something different.  The fans audibly start to power up and the power LED turns white, as if it were waking, for under 1 second, then everything cuts out, and the power button LED shuts off.  After about 2 seconds or so, the computer then starts itself back up.  It definitely seems to be booting, albeit much faster than normal (the Windows logo shows only very briefly), and then I get the login screen, and when I do log in, everything is as I've left it.

My concern is the system doing that brief-attempt at powering up when waking, then shutting off and firing itself up again.  The behavior is nearly identical as to when I got stuck in the power-on-power-off loop.  To me, it seems like it fails to fire itself up when it wakes, then shuts off.  Then, on its own, tries again, and succeeds (strangely) from the cold-start.

The behavior reminds me slightly of when a start capacitor of an electric motor is intermittently failing.

My question - what exactly is happening?  Is something starting to show the signs of failure?  How do I resolve this issue?  Did I manage to break something somehow with the attempted memory swaps?  If so, then why is the system working except for the sleep issue?  It seems baffling that a cold start behaves fine, but waking from sleep doesn't.

System is a bone stock XPS 8700 with the i5-4460 CPU, the only change is that an AMD R9 285 GPU has been installed in place of the original video card (and drivers changed appropriately - this swap was performed back when I first got the machine).