Was your logic board recapped properly? If not, then do that first, and also clean the PCB very throughly before you solder the new capacitors. They used a type of capacitors on these machines that are prone to leaking and shorting out the logic board after 15-25 years or so. Otherwise, it is also very likely a logic board problem, more exactly it could be a Bourns filter problem. So that needs to be replaced. As the Larry Pina in the book The Dead Mac Scrolls says: "Symptoms: On startup, the desktop appears, but neither thekeyboard nor the mouse work. Typical history: The problem occurred when you connected ordisconnected an ADB device while the computer was on. Probable diagnosis: The problem is on the Mac SE logic board. Solution: Check/replace the shorted fiIter (Apple part 155-0007-E) at board location A 11"
If you follow the official service manual that can be found with some googling, then why not. I’ve done it a few times myself on these machines with no problem. The only major risk is breaking the CRT on the neck itself if you don’t remove the neck board (just pulls straight). Most likely, the floppy drive itself is not broken, just in need of some overdue service, like some lubrication and head cleaning.
Few points to add: Was the logic board recapped and cleaned? Did you try and change or reseat the memory? When was the last time the machine worked properly? Last week? Or 10 years ago? CMOS battery (actually it is called the PRAM battery on these Macs) would not cause much problems on these machines if it goes flat, however it might leak after all that time and destroy the logic board…
If the disks are known good and you can boot from then on an other Mac 128K, then there is most likely something wrong with the drive or perhaps something on logic board. However, the RAM problems usually result in sad Mac with the error code. Usually there is a problem with floppy drive, as the mechanism gets stuck as the old grease hardens and the head assembly would then have a problem advancing on its rails, so it would only read track 0 properly. It is a main part of a Classic Mac restoration/repair to disassemble/clean/lubricate these old drives. I did have problems on a 128K with the boot disks prepared from disk images on a 1998 PowerBook G3 Wallstreet. It just didn’t like them, but disks that were prepared on a Mac SE/30 worked perfectly. Also I needed to use actual 800K disks, not the 1.4M ones.
As far I am concerned, these keyboards are unrepairable when they fail. Well at least you can still change the batteries in those models, the newer ones have a soldered lithium battery. Check this guide, it might provide some help: Apple Wireless Keyboard (A1255) Teardown
So, did you replace the eject mechanism gear? You must also thoroughly lubricate the other gears and check that everything moves freely. As the machine is almost 30 years old now, the floppy drive must usually be cleaned and relubricated to restore its proper function. All the rails and other moving stuff should be relubed.. Did you check that the head assembly can move freely on its rails? If not, you would need to put some lithium grease on it. This can also cause the grinding noise when the head is stuck and the actuator would try to move it. Also the main motor can rub onto something underneath, which would cause grinding noises...
Floppy drive works? Eject works? Usually the eject mechanism in the floppy drive gets stuck by the age and hardened grease and chews one plastic gear which would result in non-stop operation of the eject motor. Click on startup would trigger floppy an eject before boot attempt.
Stage light effect is usually caused by a loose or broken display cable. Sometimes it can be resolved just by reseating it. I think that if the display cable is bad, you would most likely looking at a whole new display assembly. The keys however, are the design flaw of the 2016 MacBook Pros. Usually they replaced the keyboard under warranty. Sometimes keys can be remedied by blowing them with a compressed air. Take it to Apple and try to get them fix the machine.
You have a problem with a logic board. I believe there is one chip that developed dry solder joints. Will the computer freeze if you change to the discrete GPU? Do you perhaps get a keyboard backlight to turn on when it fully boots? Try closing the lid and waking it after 20 seconds, if perhaps you get the picture.
Is the battery recognised? Do you get an X or percentage in the battery icon on the top? Will machine work off battery, albeit it is not charging it? Do you get a green light? If you do get a green light, then most likely the problem would be on the logic board and not on an I/O board. Update (09/09/2017): Interesting. So it seems like the logic board is not communicating with the charger (SMC). Could be I/O board and or logic board. At first guess, you might be lucky and it is only the I/O board. Better take laptop to Apple to have it checked.