I'm still a beginner on deep embedded systems development. I would like to know how to control a servo motor without using PWM, since I didn't actually learn anything about it on my classes and I'm not sure wether I could use it or not.
Ok, but most servo motors use a 50 Hz (20 ms period) repetitive signal, where the pulse width nominally 1-2 ms or 500-2500 us, controls the angle of the output shaft.
This is the poster child for a microprocessor PWM timer/generator.
Get the LPC2103 reference manual, and review the timer/pwm section. Any teacher worth listening to should be able to demonstrate this within as couple of minutes.