vibration in habitaculus

Hi everyone. I bought a 2004 Chevrolet Corsa 1.6 with 79,450 km two months ago. I noticed the steering wheel vibrated a lot, and now it's even worse; the whole dashboard vibrates . I started looking for the problem and changed the spark plugs because they were in bad condition, but the problem persists. I've come to the conclusion that it might be stiff or dried-out engine mounts because I tried to move the engine and it was impossible.
Could that be my problem, and how can I properly check if that's it?