If you do not want to graft another external PSU to your defective TC, you can also start dissecting it to identify and change the faulty capacitors as indicated by the chief editor of the french website lapastenague.
He replaced the 3 faulty capacitors by 2x 1500uF and 1x 470uF. Everything works fine, even though we would recommend keeping using capacitors with the identical specs than the original ones. As he mentioned it, one should pay attention to unload capacitors to prevent any electrical shock.
Apple seems to be not carefull enough with its manufacturers when specifying the quality of capacitors, going for cheap models might lead to some major impacts on its image if this new and growing issue with the lifetime of Time Capsule turns into a huge problem.
In the past, some Apple products were already affected by similar issues in the past: Airport Express, first Airport station (http://www.vonwentzel.net/ABS/Repair/index.html)
