I was definitely the first one to do that to her. I couldn't so much as see a fingerprint in there! ... if I probe the floppy port and fine the volts are good, does this mean I'm probably looking at a bad logic board?
Not to burst your bubble (again), but an ultra clean unit is gurantee that someone else hasn't violated her. :beige: What you want to look for is evidence of scraping near the bottom rear of the case where the metal chassis has rubbed against the case from where it was re-assembled. If they are present most likely it's been opened before.
It is unlikely that this Mac just "stopped working" in storage if you don't see any evidence of cap leakage. That said, there is a possibility of corrosion on the power pins as I described above. The first thing you want to do, before you do ANYTHING else, is pull all the connectors apart. This means the J4 & J7 connectors between the CRT and logicboard and the analogue board. If you see any tarnish or corrosion you should clean the contacts. Merely disconnecting and reconnecting can often fix problems like this. As Trag mentioned, pry up the ROMs (assuming they are there) check for tarnish, clean if necessary and reinsert. If that does not fix it, then off to check the voltage which you need to do regardless if these steps work to avoid a much bigger problem.
If none of that works, then you are going to hate the next step ... you are going to need to pry off the vinyl or (more likely with your vintage) cardboard panel on the outside of the analogue board. You are going to rip the original square double-stick pads all to hell, so don't worry about it. They are in the wrong places anyway, will need to be completely cleaned off the analogue board and eventually replaced. Just try not to tear the cardboard cover (which is as rare as the top metal shield).
If the cardboard cover is black, as many early models are, it's going to be much harder to check for burns to help isolate problem caps. Hopefully you have a white one. The pads will also show scorch marks since they tended to cover the part of the board that fried most often. (Bad Apple!) Then remove the entire analogue board for careful examination.
If you still don't see any obvious damage you're going to have to test all of the problematic locations with a multi-meter, or better yet, just wholesale replace all the caps – they need it anyway. Most of the time this will fix any problem (according to Larry Pina, whose book Macintosh Repair and Upgrade Guide you really need to get). But before you do ANY of that, try re-flowing all of the J4 & J7 pins on the analogue board, as that may fix any broken joints, which is a very common problem.
As I said before, this is most likely not your logic board. If the analogue board is not able to provide enough power to startup the Mac, you're not going to hear a bong. That bong tells you everything checks out, and if no power is getting to it to run the built-in startup diagnostic, then it can't very well report back. The fact that your display is dark strongly suggests the analogue board. It's too bad you don't have another logic board to throw in there though just to rule that possibility out. Even if you get the analogue board checked out, there's no guarantee you wont have problems on the logic board too.
Not to discourage you but I have an early January 128K in pristine condition as well, with the same original features as yours and looks like it has never been opened, except that it has ... someone checked every connection on the back of the analogue board with a multimeter as evidenced by a red marker used to check-off each solder joint for component tested. And I'm here to tell you after repeating much of this work, mine is no closer to working than it was before I tested every component on it. The CRT works, the logic board works, but the analogue board just doesn't. Because it is in pristine stock condition, I have not yet replaced all the caps as it is sort of a "time-capsule" representation. I did desolder the flyback and found it works perfectly on another analogue board and a known working one did not fix the problem on this analogue board. So whoever tested mine originally, just stuck it on a NF pile, rather than put any more time into it, and it was never touched again until somebody cleared it out of storage and I bought it on eBay.
Hopefully, you dod not have a similar situation, but if you do, you're in for a lot of work (one of the reasons I haven't just replaced everything on mine too). If it gets this far, you might just want to buy a new analogue board, especially if you intend to actually use your 128K.
The only way to really test your logic board and analogue board independently is to get another compatible Mac. A Mac Plus is a good Mac to have because thy are cheap, they can format 400K disks and have SCSI access which is one of the few ways to transfer files between a modern Mac and Mac lacking a SWIM. Pick up a good working one off of eBay and then swap out the parts. This will at least pin down your problem and give you a working analogue board for your 128K if that's indeed the problem, while you repair the old one.