2002 Chevy Impala Radio Doesn't Work

Jeanell, If engine is truly locked up, you have a few choices, find a good used engine from auto recyclers/wrecking yard, have engine torn down and rebuilt, have new engine installed, scrap car and look for another vehicle.
If vehicle is overall good/excellent condition and brakes,tires,suspension,exhaust,etc. good, the most cost effective would be to have a good lower millage engine from auto wreckers installed, some auto wreckers also do the install and guarantee the engine and their work.
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Why do think the key security is bad? If you still have a factory key, this is not the problem...if no factory key, you can take your VIN number or original key to GM dealer to get new key that they will program for you...Check for dirty battery connections:)

If it is built without it then all you can do is this: http://www.bulldogsecurity.com/Products/453055507-model-ke1702-vehicle-keyless-entry-system.aspx If it is built with it then the ones you bought will not work. you will have to goto the dealer and get them programmed for the car. you cannot do it yourself

If you need further help, reach me via phone at https://www.6ya.com/expert/steven_a67ead41eb5fc62a

check the fuses there are shared fuses for all these items you mentioned and the radio uses more than one fuse

I think you could use this manual method instead.. My nephew used
it to repair my car and it's totally perfectly fine now. Here's the website he bought it from. www.reliable-store.com

You will need to have the switch replaced.

Check your owners manual for the location of a SECOND radio fuse. There are usually TWO fuses for the radio. One is the for the circuit to operate the radio when the ignition switch is turned on, the other is when the switch is off. The second one provides power to the radio when the key is off. It keeps the clock running and your radio presets. The radio requires BOTH fuses to operate properly.

Good Luck . . .

output side of radio could be bad,use fader control to check each speaker, if no sound have radio checked

This may be a anti-theft issue. If it is and you want it fixed, the Chevy Dealter is probably the best place to have this work done, IF it can be done at all. My Chevy radio instructions tell me that if there is a genuine power loss to the radio when the anti theft system is activated (like someone breaking into the car and stealing it, cutting the wires) that the radio will not work again with out GM intervention.

Anti theft problem Ignition lock cylinder or Body control module