I recommend cutting up a piece of flat, thin plastic (such as a milk bottle) in to shims. Then once you've lifted up the plastic on the battery, slip the shim underneath to keep the clip up.

Even once all clips are released, it takes a good deal of force to separate the two halves of the case.

Be very careful when releasing the clip between the tower and screw hole, as a slip here could damage the PCB, preventing repair.