You'll probably need to recreate the gradients.
Sometimes, saving from CorelDraw does that to gradients.
But if this trick can make it faster for you to re-work the gradient, you can delete all the "inside" little lines/square (the ones you see as square in the outline view) and keep the ones that serve as clipping mask on the outside edge of the gradients. And then you should be able to re-apply the gradient properly using the same "skeleton".
You'll probably need to keep the original version opened next to the new one and use the color picker to get the exact same gradient colors for every element.
If you don't think you'll ever need to make this into a pantone and can use it in CMYK, then maybe you could try to use the "pathfinder" and "divide" all this. That won't make a clean job as re-doing the gradient but at least the logo should still be less annoying to work with than it is right now.
If you want to have less paths, than the first option is the best one.