The power LED does not light and the Maximite draws very little current (normal consumption is 125mA). Capacitor C5 (in the Maximite) or C3 (in the mini Maximite) is nearly always responsible. It must be a low ESR Tantalum or ceramic capacitor (NOT aluminium electrolytic) since the PIC32 is very sensitive to its characteristics. If you suspect C5, try replacing or paralleling it with a higher value and/or a higher working voltage (both of these will improve the ESR). The best solution is to solder a surface-mount 10µF ceramic capacitor with Y5V dielectric (available from au.element14.com) between the solder pads for C5 (or C3). The kits from Altronics or Jaycar should not have this problem but it is worth a try.
Using USB power as the power source is the cause of many problems with varied symptoms. Many computers or hubs cannot supply clean power so before you try anything else, plug an external 9V to 12V power pack into your Maximite and test it.
Errors reading or writing to the SD card. This has proved to be an on-going issue with about 5% of cards and I have not got to the bottom of why some work in the Maximite and others do not. Some cards have buggy controller logic when used in SPI mode and this may be the reason. The only solution is to try a few different cards. A list of cards that are known to work is available at duinomite.com/Maximite-control