Asus G74SX, Intel i7, Seagate ST1000 hybrid drive
Win7 Home Premium, FRESHLY installed after new motherboard installed.

Problems/symptoms:
When you shut down, Windows shuts down, screen goes black but power light stays on. computer is still on. The 'innards' are still on, as the battery will die unless you do a hard shutdown after screen goes black. BUT, when you start up again, it does so normally & does not start in safe mode!
When computer goes to sleep mode after inactivity, it will not wake up when you push buttons (any of them). Hard shutdown again needed, but in most cases, it starts up normally (no safe mode).
But when you do a restart, the computer DOES actually shut down & restart automatically. But it's a little 'off' in that the screen blackens & the power light stays on 10 seconds or so before it goes off & then restarts normally (normally the light would go off the instant the screen goes black).
Factors to know:
Computer bricked several months ago; at first, everything would freeze after about 1 min after boot. After lots of hard shut downs, got to point where it wouldn't boot at all & screen would be black, but it was still technically 'on' (edge/backlights were active, not pixels). No BIOS, no startup screen, just...nothing, save for the fan running at high-speed & the drive sounding like a drive.
HDD was new & worked fine when I hooked it up to my desktop via an external drive 'kit'. Bummed at idea $1100 laptop might be a goner, but went for a hail mary & got a motherboard on ebay...made sure part # matched, installed it, put in old drive & it surprisingly fired up fine, except that the power issues mentioned above appeared.
Read up on this, and saw somewhere that regardless of whether it looks OK, it's always a good idea to do a clean install after a motherboard replacement, so I did that. Something odd happened here; after initial install, it would power down fine when you hit "shut down"...so I thought I had fixed things!
BUT after several rounds of the expected "Windows Updates"...I think it was even the day after the install...the power issues kicked in.
Searched around for ideas/suggestions/similar issues, and someone said a BIOS update should fix it. I updated to the latest BIOS, obtained from Asus site...went like a charm, didn't fix the problem.
I've looked at some Event Viewer logs, and you'll see errors, but the time of the events show that they're usually due to the hard shutdowns. And I really don't know what to look for there, either.
That brings me here, to the wonderful people who have helped me out with several pesky viruses (viri?) in the past (other computers, this one's been a charm, until now). Any ideas? Do you need any more info or clarifications?

I guess...as problems go...it's not the worst thing in the world; it works great when it's 'on'. And I could live with the hard shutdowns too...when I'm actually shutting down. But it's really the 'not waking up' that's a giant PITA.

Thanks for your advice!