Wow...it really is stapled. Probably not glued either. What a piece of junk...and not 2x4 but just 1x4.
How about this project: Cut a couple lengths of 2x4 to fit snugly at each end, underneath the shelf, running from back to front and screwed/glued to the existing end pieces. Do this for both top and bottom shelves, so 4 pieces. Then, cut 4 more pieces of 2x4 to fit snugly, lengthwise, between the first four you just did. So, essentially, build a couple of frameworks out of 2x4 that fit tightly underneath each shelf, and screw/glue them to the inside faces of the existing shelf frameworks. When you're done they won't even show, but they will significantly strengthen this thing.
I would be sorely tempted to install a few screws into all those joints that show only staples now. They won't be beautiful...but neither are the staples. At least the screws will be doing something.
Places like IKEA sell simple metal X's, just two small diameter metal rods held together by one screw where they cross. The IKEA ones are meant for their ivar shelving. They install on the back of the unit with four screws, one at each end of both pieces. They are quite low-profile and discreet, and dirt-cheap, but add a huge amount of three-dimensional stability. Takes about 5 minutes to install one, and I think one of these would be the minimum required bracing for this project.
Finally, at risk of sounding paranoid...IKEA also sells a little kit consisting of a couple of screws and a strong woven nylon strap, to affix tall, top-heavy pieces of furniture (like this one) to the wall to prevent tipping over forwards. The kit has drywall anchors to allow installation anywhere, but for this project I would put two of these straps on and screw them directly into wall studs. You could centre the stand on two studs, so that the straps would be behind the tank and not glaringly obvious at the corners.
When you finish, this project will not be as strong as one you could have built yourself for a fraction of the price, and it won't look any better, but it will be sufficient. I apologize for the constant use of the term "project" but unfortunately that is what this expensive and currently useless fixture is going to be. Good luck!