Trouble keeping car running after changing battery

First, take the vehicle to autozone, or advanced auto parts, to have your codes read for free. This will point you into the area you need to start testing. Next id perform a few simple tests for the charging system. Start the vehicle with as normal, disconnect the positive terminal, if the engine dies the suspect component is the alternator. Step two, if the previous test passes, reconnect the positive terminal and disconnect the negative terminal, if the engine dies you may have a loose engine block to chasis ground. If it passes the basic electrical checks, it could be a number of things, clogging fuel filter, bad injectors, injector fuses, a failing fuel pump, dirty pickups for the ignition system, etc, etc.