I have an NES that powers on but does not play games. I get a solid color onscreen. I have cleaned the console thoroughly, especially the 72pin connector, and have cut the 10-nes chip pin.

I am not sure the actual part name (RF modulator?), but the metal box on the back-right corner of the motherboard which houses the coax and composite hookups is rusted. I believe this is the main issue. Is there a store that sells this part?

I've thought about bypassing the box altogether, but I have no idea how to do that or if it is possible at all. Has anyone tried this or can direct me to a turtorial which covers this topic?

if you getting a solid color on your screen your system is working sounds like you need to restore or replace your 72 pin. its also possible the pins on the motherboard have some corrosion on the pins that will need to be scrubbed of with some superfine steel wool. if none of that works you have a bad trace on the board. if you want to bypass the box completely you need to install one of these
http://retrorgb.com/hidefnes.html...

but you need a good soldering skills to do this.

You do need to be able to solder/desolder well, but I thought I'd point out that desoldering the RF module is even harder, so your suggestion works regardless.  
 

true^

Sounds like a possible dead PPU or CPU.

Bad RF boxes usually display a snowy picture (not solid colors). Also you would still see video and hear game audio.

I always clean the board connector as well as the 72pin thoroughly. I took your advise about sanding down the teeth on the board connector with a fine grain sandpaper. I didn't see any major corrosion, but thought I should at least give it a try then wipe up the dust.

I still got a solid green picture.

I thought, 'What the heck; I'll replace the rf box with one from spare NES.' I did that and still got a solid green picture.

I did a scan of the board and didn't see any scratched traces. I admit I could have been more thorough.

What's the procedure now? Test voltages? In what order and locations should I test? Also, what values should I read?

You can test your +5V power. You can use the pin 16 of the cic on the motherboard from test to this voltage. You can check also the reset pin of the cpu (pin 3). You are supposed to have low signal(0V) if the nes is working when game in.

ok but did you try a new 72 pin?  other than that it could be a bad cpu or ppu like retrofixes said.  whats the the condition of the outer housing of your nes? any broken or cracked corners?  yellowing?  mayjor scratches? cause if you cant fix it ill buy the nes case off you cause i need one to build an nes computer.

To "bypass" the RF box, wouldn't you just use composite AV from the side?

I am talking about the internal RF box (the one soldered to the board). Even so, I think the concern is irrelevant anymore due to me desoldering the current one and replacing it with another.