You’ll have to post a photo of your wiring for anyone to help you with that.
As for the ohms and wattage ratings, it’s a bit confusing, but I’ll try to explain…
The CanaKit amp is rated 7W @ 4 Ohms when connected to a 16V supply. This means it will put out 7W of power if connected to a 4 Ohm load, if supplied with 16V.
The load is your speaker. Ohms is a measure of its inductance. (When I say inductance, just think resistance, inductance is the amount of resistance to alternating current.)
Now the amp can’t just shove as much power into the speaker as it wants to. The amount of power the speaker gets is limited by the inductance it has, much like how you can limit the amount of water that flows by turning the handle on your faucet.
So, if you connect a speaker with a higher impedance to the amp, LESS current will flow and you’ll get less sound. Connected to an 8 Ohm load, your 7W amp becomes a 3.5W amp.
Another thing you should know is that if you connect multiple speakers, you change the amount of impedance the amp sees. If you connect two 4 Ohm speakers in series, they act like an 8 Ohm speaker. If you connect them in parallel, they act like a 2 Ohm speaker (Ohms / Speakers, assuming all speakers have equal Ohn rating).
Connecting a 2 Ohm load to an amp rated for 4 Ohms would be bad. The 7W amp will try to put out 14W, and that could cause any number of problems. It could blow the amp immediately or days later, it could cause it to go into thermal shutdown to protect itself, or it could cause the sound quality to be terrible. It’s impossible to know for sure unless one studies the datasheets for the parts it uses to see what hey can handle.
Now some folks I know have connected their amps the wrong way and have gotten away with it, but remember the 7W @ 4 Ohm rating is for an 16V supply. If you supply less than 16V the amp is going to put out less than 7W of power in the first place, and maybe the amp will survive a while. Turning down the volume because the amp starts to distort above a certain volume would also reduce the power output, further protecting the amp. In fact, it may be that with that amp, if you exceed the max power output it distorts, so what you’re hearing is a direct result of exceeding the amp’s output power by connecting a 2 Ohm load to it. But I digress.
The other thing you have to worry about is your speaker’s wattage rating. You say your computer speaker says 4 Ohm 3W on the back. That’s less than 7W, so that’s bad. It’s bad because the speaker itself can be destroyed, and if it’s destroyed it might take your amp with it because when it melts it will short the amps outputs and now you have a 0 Ohm load connected. Bad times for all involved.
However, remember what I said earlier about connecting two speakers? If you want to, you could connect the speakers in series, which would increase the load to 8 Ohms and the amp would put 3.5W into that if you have a 16V supply. That’s still more than 3W, but since if you are running off 12V the output would be something less than 3.5W, and we can calculate that like so: 12V / 16V = 0.75, 0.75 * 3.5W = 2.6W. So you’d be good to go.
Do NOT connect the two speakers in parallel however. If you do that, they would become a 2 Ohm load, and then BAD THINGS would happen.
(Note that if you had a different amp, or 8 ohm speakers, connecting them in parallel might be okay.)
I would look for a motorcycle amp. Those would be designed to run off 12V, so you should get the full advertised wattage. But again, not from AA batteries.
