A few points you may wish to consider:
It requires a proprietary video switchbox, which is a pain to get ahold of. The video switch box turns the system on and off. If you don't have one of these, you are without a paddle.
It requires a proprietary Magnavox cable. It is similar to that used by early models of the Odyssey 2. It looks like a straight prong.
The system uses Magnavox Part No 1A9179 Input 117V AC 60Hx 3W and Outputs 9v DC 40mA. The connector is, um, 1/16 inch I think.
Cartridge 2 is a fine cart to test both controllers with. You should be able to see both controllers move when this cart is powered up. There are no other graphics aside from the dots that the controllers move.
Be very careful when you try to clean anything on the system, especially the faux woodgrain on the controllers. Windex or Mr. Clean or any Benzene based cleaner will remove the woodgrain and letter clean off. Even wiping the cables without any solvent tends to change their color. Beware!
Reseating the cart may solve many of your problems. The connectors tend to lose contact over the years. And these babies are old.
And from the FAQ:
4) What items came with the Odyssey 1? The complete list of regularly included items in the Odyssey 1 (One) Packaging:
Hardware:
Master control unit (ITL 200 1of 4 pcs.)
2 Player control units (ITL 200 1of 4 pcs.)
Game cord (ITL 200 1 of 4 pcs.)
Antenna game switch with 2 hanging hooks (ITL 001) came in its own
box.
6 red-label Eveready C batteries
Game cards #1 #2 #3 #4 #5 and #6:
#1 Table Tennis
#2 Ski, & Simon Says
#3 Tennis, Analogic, Hockey, & Football (for passing & kicking)
#4 Cat and Mouse, Football (for running) & Haunted House
#5 Submarine
#6 Roulette & States
Overlays (2 each, one big and one small for different televisions):
Anologic
Cat and Mouse
Football
Haunted House
Hockey
Roulette
Simon Says
Ski
States
Submarine
Tennis
Standard game accessories:
Stick on numbers (642978-2)
Football Game board field/Roulette Layout board (642898 0001)
Odyssey stadium scoreboard (642964-1)
2 Football tokens (attached to the Odyssey stadium scoreboard)
2 Yardage markers (attached to the Odyssey stadium scoreboard)
20 Pass cards
20 Run cards
10 Kick off cards
10 Punt cards
2 Pass card
2 Run card
2 Punt card
30 Clue cards
13 Secret message cards
50 chips (16 red 16 blue 18 white) with ziplock bag
Money (approximately 100 each of $5 $10 $50 and $100)
28 Simon says cards
50 States cards
Affairs of states (answer folder) (591549-1)
States study map (591550-1)
Pair of dice
Loose documents:
Odyssey installation and game rules book (IB2622-2)
36p ("Run 1 a" and "Run 2") 1972
24p ("Run 1 b") 1974
"How to get service" card (EL2811-2)
"Thank you" card (EL3018-1)
"Notice" card (EL3028-1)
2 key punch inspection cards
A coupon that promised "free games" with registration (Percepts?)
Now have fun!