LCD inverter, backlight or something else?

It should be safe to connect the tube from the 573zg to the 5738zg. They are very close in model it seems. If I were you since you are going to be back there anyways, take the laptop apart. Inspect the areas that you heard the noises/smell. Check inverter location, inspect inverter. make SURE you find the area where it fried and replace that component. Its better to take it apart and inspect the entire laptop. Either it failed from defect/old or something caused it to malfunction.