Chances are, when you dismantled the cabinet something broke, or you only had 3 things out of 4. The other problem you will run into is with light fixtures where they are very odd.
Light Fixtures - If you cannot get replacement parts for them, you will need to go to Home Depot and buy a new Florescent light fixture to replace the odd ball one. The ones I use cost around $20 and are 19" - 21" depending on the cabinet. Before you go through all the work of replacing the fixture, get the number off the bulb and take the starter to your hardware/light store and see if you can get replacements for them. The number on the bulbs will be something like 15FT or the like. I would Google for the information as well. You can find most of the bulbs and starters online, including those for Nintendo games.
If you can get replacements, then just buy new bulbs and starters. NOTE: Before you just go and put a new starter and bulb in your light fixture, you need to read the Tip & Trick on Checking Your Light Fixture. This will keep you from blowing a fuse and killing a new bulb and starter. If you do replace it, I suggest splicing the power cords from the old one and the new one together as the new one probably wont have a long enough cord on it.
You can use the box splicers (I like them cause they are easy) where you put both wires in the box, and crimp it shut. Quick and Easy. If you want it to look seamless, then you can solder the wires together and put heat shrink wrap around them. This looks nicer, but it also takes a lot more work :-) You should also pay attention to the voltage on the old light.
Nintendo uses a 100V light and my replacement was 118V. What I had to do was connect the light to the power block prior to it going into the transformer. If you don't do this and you try to use the outlet where the old one was plugged into, then the light will sit there and flicker. Sometimes it might come on, but most of the time it wont.
I have pictures of the inside of my Donkey Kong on the Popeye To Donkey Kong Conversion page.
Power Supplies - These days I make it a point to replace the original linear power supplies with a switching one only if the original power supply is unreliable, or it was completely missing. The reason is that a new switching power supply will be more reliable (some people will argue this point) and easier to replace if it dies. I keep the original power supply in the game so that if someone really wants to use the original power supply, they can.
Use the old power bricks for the Monitor only if you put a Switcher in.
Buttons, Joysticks, other Controls - If you can find replacements for these that are in better shape, then replace them. If the color of the buttons are wrong, you may want to try and find buttons that are the right color.
Coin Doors - My Donkey Kong has a Coin door that is bent where someone tried to break into it. It was also modified so that it has a button on the front of it for Free-Play instead of using quarters. I am going to replace it. The one on my Robotron looks pretty beat up as well and will probably be replaced.
Wiring Harness - If you have the luxury of having one and its in good shape and it's for the original game, then keep it. If not, then you want to replace it. If you can find an original harness on the Internet or from an OP then you should buy it. Chances are you wont. In the case of Stargate and Robotron I am going to build a new harness form a JAMMA harness.
Harness Loops - These are the little plastic (Metal in Nintendo) loops that hold the Harness in place. Most of these probably broke when you removed the harness as they get brittle over time. You should be able to find these at Radio Shack or a hardware store. I replace them just for good measure.
Speakers - These should be easy to replace. Just look at the back of the speaker and on the magnet should be printed the power rating (in WATTS) and the Resistance (In OHMS). For example: You're speaker might be 10W @ 4 OHMS. If you're still not sure, just take the speaker down to a car audio place (best place to find these speakers) and let them look at it. You should always replace the speaker with the same ratings.
Marquee, Front Plexiglass - These are hard to come by, if you have one that is in "B" or better condition, you will probably want to keep it unless you can find one in better condition.
Control Panel Overlay and Side Art - Most of the time, you'll have an easier time finding Jimmy Hoffa than finding a replacement for this. Post a message on the forums, call OPS, pray, and then consider getting a reproduction or 3rd party replacement.
In the case of Side Art, if its a Williams game, chances are, it was painted on. This is a good thing in that if you can find someone (or you are artistic enough) you can just paint new side art on. A lot of the games, however, used stickers as side art. Some of the places I would check for replacement are: Phoenix Arcade and Game Stencils.com
There are several more places to check, look on the left side-bar for the links.
All these new parts, now its time to Re-Assemble it....