So perhaps you could ‘hide’ the enter-to-submit button not by making it disappear but by pushing it off the page where it can't be seen, and then catching the click event on it to return false and stop the form submission. (This is a bit ugly, but hiding it via display or visibility will stop it working in some browsers.) If you don't want this button to be displayed, you can position it with a large negative left value to push it off the side of the page. So it is in general better, when you want to control the default submission action of a form, to put an extra button in as the first submit button in the form. If you miss a case you will get accidental default-submissions if you hit a case you shouldn't, you'll get accidental enter-submissions. Whilst you can attempt to catch Enter keypress events manually it is highly unreliable to do so, since Enter isn't always supposed to submit a form, depending on (a) what type of element is focused, (b) whether shift/ctrl+enter is used, (c) what other elements are in the form and (d) what browser it is.
If it does, it might be time for you to get yourself a new keyboard.
Check if the problem remains after plugging the keyboard into a different computer. Unfortunately you can't change the ‘default’ submit button in HTML, it's always the first input/ button with type submit/ image. If your enter key is still not working, then it most likely is an issue with your hardware.