Nice! I got [overly] determined after posting this query, and carefully worked my way up each side toward the top of the remote with a small flat-blade screwdriver, quite easily popping it completely open with no exterior scarring (but some decidedly cracked interior plastic-tab housings).

Nicely basic interior parts: the grey rubbery plate housing the remote's individual buttons (which fortunately stayed locked in their housing's sockets), and a circuit board on which the bottom of the black buttons made flat contact. Immediately noticed an oily residue buildup on the buttons' contact area with the board, especially in the lower half of the remote (the remotes reside in a high-humidity marine climate), so in a couple of passes wiped them and the adjoining circuit board face dry with some pedestrian Kleenex tissue, removing a noticeable amount of blackish residue in the process.

Popped the 5-piece son of a gun (two housing halves, circuit board and button plate, and IR beam red-plastic shield) back together, and like Lazarus from the grave, it's immediately and totally revived. Did see only one candidate on the circuit board's reverse side for an internal battery/capacitor, a small 2-contact yellow cylinder the size of half a Contac cold capsule (whatever happened to those?) soldered in place, but the contact cleanup job did the trick.

Moral of the story: humidity/age-related residue built up on the button bottoms' contacts with the circuit board, apparently shorting out the unit enough to render it inoperable [as in no lights/no functionality). Another 10 years' life out of this beauty? I hope so. Even with the broken tabs, the unit snapped back together solidly, and the two screws are holding it in place (until the next time I drop it on a hard floor, perhaps). Thanks anyway, hope this home-repair venture can help someone else in remote-control resuscitation!