Is there a way to force an application to start automatically on every power up on my Samsung Galaxy S7562?
There are several apps capable of doing exactly that (adding other apps to the "autostart ramp"). Some of them you can find in my Auto-Start Management listing. I'd recommend you taking a look at Autorun especially for mainly two reasons: 1) it's the best rated I've seen so far, and 2) it's pretty permission-friendly (only requesting 1 permission: to be informed when the device boot completed). Quoting the app description:
A simple autorun service that allows you to automatically launch selected applications upon your device power up. No more missed messages because you forgot to start your favorite chat client, just setup an autorun and always be online.
For alternatives, please consult the list I've linked above ;)