I found some info online about bad capacitors in Asus routers, so I decided to investigate. I chose to first look at the router, because it is easier to open. That just involves removing the glued on rubber feet, unscrewing the Phillips screws that were hidden by the feet, and lifting off the top. I immediately noticed a bulging capacitor near the toroidal inductor near the power input. It's used for filtering 3.3V power, so it's quite important.
I opened up the wall wart by hammering a blade into the seam at various locations. This was much quicker and easier than sawing it apart. Then I had to yank out the circuit board, which was glued with silicone. The 1200µF 10V output filtering capacitor was bulging and leaking. After replacing it, the, voltage droop under load became much more reasonable.
This wasn't too hard, but I shouldn't have to deal with bad capacitors in a product manufactured in 2008. I'm disappointed with Asus. By 2008 they should have learned how to avoid this problem. I guess the capacitor plague continues. Wikipedia even has an "after 2007" section in the article.
Finally, here are photos of markings on the two bad capacitors. The obscured number at the top is 8011D.