We are talking about a -001 kit, do we? When you look at the schematics (in the appendix of the user guide), you see that the 3.3V regulator is powered by the 5.0V rail, and the LED is too. So this is kind of strange. It might be that just one of the capacitors on the PSOC5LP module got damaged, causing this behaviour (but it might be the PSoC itself, who knows...)
In any case, you can order a PSoC5LP module separately: http://www.cypress.com/?rID=43673
Part number you are looking for is CY8CKIT-010A.