I don't know how much help it is, but I have recently aquired a NES,
which seemed to be not working at initial testing and inspection.
It appears to only give blue screen. The CIC is operating correctly, aparently though.
The cart connector is in realatively excellent condition, not bent or scraped by any evil Game Genie (with its overly thick pcb and nails on chalckboard death grips). Only the fingers on the motherboard to the cart connector shows any slight deformities (a small fraction of what old 8-bit pc or colecovision board traces look like, and what seems to be a thin bit of oxide film on part of just a few of the motherboard's fingers for to the cart connector).
I did a mild clean with 99% iso-propyl alcohol and a soft toothbrush, but didn't notice too much dirt or grime generally, the most of the main board looks good, was a bit of tin/oxide around one or two through hole solder blobs, but I brushed at it and finished it of mostly with my fingernail to be gentle on the board.
Nothing on the mainboard smells funny.
The RFMod/Power Module definately has a some noticeable pungent chemical odour.
I began to worry it could be a fault in the PPU or CPU, but after much searching for
blue screen repairs online and finding none of them useful or relevant, and just
poking the multi-metre at all the chip powers and grounds and the reset and main
power routes and the 7404 inverter and the CIC and resigning to order a cap kit,
my brain started working on it's own...
I recalled one of the many repair videos I watched mentioning a slow bootup,
and (either the same or another video) saying if left on after a while it would boot
a game.
So I decided to just for kicks, play around with waiting, powering off a while and powering on and just leave it alone, or different on/ off/ wait times between.
Wouldn't you know it, it's been able to boot, with all the sound and graphics working fine (at least with RF-out so far, haven't lucked into it booting with A/V-outs yet)
I have noticed the 7805 and it's heatsink are burning hot-ish, fairly hot, not impossible to touch, but longer than a few seconds might result in a mild burn.
Also the 5v rail is closer to 6v or a hair under 6v. My meter has a slightly low battery,
but this seems like it could be high enough to be glitching out all the 5v logic, probably not enough to damage anything, but plenty to produce unreliable operation, here manifesting as unerliable bootup. The CIC operation is alway reliable nevertheless.
I haven't taken a scope to anything yet. But it seems like probably the 7805 maybe
was damaged slightly. I purchased this NES recently with a lot of other consoles with mild use from sitting in a closet since kids moved out years ago. The NES and 1 cart have evidence of being from Value Village (long before price gouging). The NES didn't come with a power adaptor, neither had the slim ps2 in the lot, but there was one oddball 12vdc higher current switching chinese made power.
My guess is maybe a higher voltage was fed to the 7805, which increases the heat dissipation, since they "burn off" the excess voltage as heat to regulate the 5v.
I haven't desoldered anything in the NES yet, but suspect either caps and or the 7805. There's a handful of surface mount caps and resistors on the underside of the RFMpd/Power Module board, frightningly the caps appear to be of various shades. My past experience lead me to think they should all be the same colour and that heat will darken them, or blacken them when they burn out.
I think I need a schematic of the RFMod/Power Module, hopefully it's not too difficult to recreate one from scratch. I have other NES consoles which seem only to be cursed by Game Genie'd cart socket connectors (ie no other anomalies).