I replaced my 1998 toyota avalon ignition key cylinder, the keys that came with the new piece do not start the engine. Do I need to go buy one of the expensive keys?

You mean one with the chip ? Yes you will need one of those to start the car

Take it back out, send your old keys with the new lock cyl to a locksmith. He will re key it and you can use your old immobilizer keys in the new ign cyl.