Firstly, loose the caps
'Only detects some tiles' is pretty vauge. Try and narrow it down to something more specific. Your first test should probably be to draw all of your bounding boxes to test if they really are where you think they are.
The test between 2 bounding, axis aligned boxes should be trivial but theres plenty of references on the 'net if you look. More likely is MyGame::collisionCheck() method being the culprit. Are you just checking for a single hard-coded other object, or is there multiple ones in your level? If multiple, then make sure you're checking all the tiles you're overlapping with, not just the one you're actually on. If theres just the single then definatly investigate your intersects() method in detail...
(oh, and whats with the _variables prefix? Looks like the old C style of labling member variables
, but i've never seen anyone use it for Java before..)