Issue starting engine

I have an Aveo 2004 1.6. 52000 miles.
Something blew out when I was trying to remove the battery cable from the post. I made a circuit with the boddy frame as I saw sparks.
Battery died and would not take charge anymore, so I replaced it. C
hecked all fuses and they look oK. I don't know how to test the relays.
The fuel gage does not move (I know the fuel tank is not empty).
I don't see sparks going from the coil to the wires, nor do they show from the wire to the spurk plugs.
I'm not a mechanic, but at the same time, I'm tryignt to avoid having to pay big bucks to a mechanic if I can find out what the problem is and hopefully replace what ever parts if needed my self.
Can someone please referme as to what could be wrong?
Thanks,:(

My recommendation would be this:

Since you replaced the battery, you know the main power to the car has been replaced. Grab a tester and start tracing your wires.
Keep tracing the power the starts at your battery and see where the power flow stops.

First thing is put your key in the ignition and turn it to the on position, but do not start the car.

Does any of your lights in the dash come on.

If not, your ignition coil relay is not activating. One of two things is not happening, either the relay itself is bad, or the power that energizes the coil in the relay is not getting power. If there is no power, there is something bad from your fuse box to the battery.

If there is power, then try replacing the relay. You can check the number on the top of the ignition relay and see if any of the other relays match the number, then pop out one and replace with another and see if it works.

Another thing I would also check for is to see if any damage to your ground wire has been done. This wire connects from your main fuse box to the frame of the car.

there is a big fuse on the positive side connector of the battery 100 amp i think and it is not easily blown amd difficult to check. check that out first (you probably) have and the negative groundong strap on these cars are really iffy does any of the electrical work ?