You dont know where the kill switch is? How do you even know there is a killswitch then? and you need to get a hold of the previous owner to find out if there even is one.
If it doesnt have one, then chances are either your fuel pump relay is bad or the actual fuel pump is out.
Anyone smart is going to hook their kill switch to the fuel pump. One of three ways, either relay, in line fuse, or the actual power wire itself. find where its hooked in at then you can follow it to the switch. You say you think its through the ignition somewhere, if there smart they would either do the power or the "ignite" wire. (anyway through the ignition if dumb) take off the plastic casing and follow the wires as far as you can, because at a certain point they cant cut into them.
some troubleshooting you can try
1. Open the gas door and take the gas cap off and have a friend listen while you start it. If you hear a click out of the gas tank, the pump is fine.
do the same for the relay. And just cause it clicks doesnt mean it works. But if it doesnt click, start there. If it does, get it tested at oreillys or autozone, they should charge you
2. Look under the hood at the relays and see if the the fuel pump relay has any wires coming off of it that look different from the rest. If it does, follow it to the kill switch.
3.Once you find the switch, leave it if you want(I would) or just unhook the wires from it and connect them to each other. They wont run the power and ground through one switch.
4. A word of advice for next time you buy a car. If it has a car alarm that works, leave it alone or have someone that knows exactly what they are doing to remove it. If it has a kill switch, make sure its done right before you buy. Learned both of those the hard way