Hi FroBro! This problem sounds like when you depress the string, it is lowered and touches the fingerboard, so it can’t vibrate. This indicates the set up between violin neck angle, bridge height, and strings is misaligned. This is rather common on really cheap violins. The problem might be fixable with a new, fitted bridge. If you buy a new bridge, it needs to be fitted to your violin and at the proper height by sanding it down to a perfect height and curvature to match your violin. Even with this done, it might not fix the problem.
At the far end of the fingerboard, there is a little piece of wood called the ‘nut’, just before the opening of the peg box. It is usually elevated very slightly higher than the fingerboard. Its purpose is the raise the strings a little, so when you press fingers on the strings down there, the strings won’t touch the fingerboard. So the nut, the bridge, and the angle of the violin neck all contribute to the relationship of strings to fingerboard.
I would ask how much you paid for the violin and if you bought it recently, I would return it with explanation of the problem. Fixing it would probably cost more than the value of the violin. I’m sorry to say it might be bad news about your violin. Let me know more details if you think it’s something else.
The Gia Rosana Violin at SuperiorViolins is on sale at the moment for only $145.00. I have been evaluating this and other violins from superiorviolins.com. This violin is very well made and comes with a satisfaction guarantee. If you can’t pay for it all at once, they offer a payment program, or provide financing for you with no interest for 6 months. You can try before you buy too.
The Gia Rosana Violincomes with bow, case and rosin.