To help the next electronics hobbyist who encounters this problem, here's a step-by-step guide to how I replaced the capacitor.
Because it can't go without saying, you follow these instructions at your own risk, and I accept no responsibility or liability for any loss or damages to yourself, your Homecast HT8000 or anyone or anything else.
Also, read these instructions in their entirety before you even think about following them. You'll need to get hold of a replacement 10V 3300uF 105° C electrolytic capacitor. I bought a 10-pack from China on eBay for just over AUS$4 (in this mad world, buying 10 was cheaper than buying 1). I also recommend you get a new CR2032 battery to replace the one on the motherboard.
- Disconnect the PVR from the mains power, and remove any cables attached to the rear of the unit.
- Move it somewhere well lit, with lots of working space.
- Undo the seven screws holding on the cover, as indicated in the image below, and remove the cover.
- Carefully, making sure you don't put your extremities inside the case, plug the unit back into the power and turn it on. If the fan doesn't start up, you'll need to get a new one. The forum posts mentioned that the fans in many early Homecast HT8000 had given up the ghost. Fortunately my fan was still is perfect working order.
- Disconnect the unit from the mains power, and put the cover back on.
- Let the unit sit around for a day or so the ensure that the capacitors on the power board have drained, so that you don't get a nasty shock later on.
- Remove the cover again.
- Refer to the image below. Disconnect the power connector (1) and SATA connector (2) from the hard disc drive. Disconnect the fan power connector (3) from the motherboard. Undo the four screws (4) holding the hard drive mount in place, and remove the hard drive assembly.
- The fan will probably be coated in dust. If it's still in working order (as per step 4), give it a reallygood clean. Otherwise, replace it.
- Refer to the image below. Mark one end of the ribbon cable plug (1) connecting the power control board to the motherboard (so that you know the correct way to re-install it), then disconnect the plug. Disconnect the plug connecting the power switch to the power control board (2). Undo the four screws (3) holding the power control board in place, and remove the board.
- Note the CR2032 battery (4) in the image above. I suggest you replace it with a new one while you're in here.
- Examine the power control board. The various forum posts I read on this topic were an accurate reflection of my problem; capacitor C12 had given up the ghost. Note the "bulging" top in the images below.
- Make a careful note of the orientation of the old capacitor; you'll need it to ensure you install the replacement the right way around.
- Remove the old capacitor. Turn the power control board over and align it to match the image below. The forum posts mentioned, and I can confirm, that the solder used here has a higher melting point than many fixed-temperature hobbyist soldering irons can reach. Fortunately one of my work colleagues had a variable-temperature iron I was able to borrow. Melt the solder and remove it with a solder sucker or equivalent.
- I needed to clean the component side of the board where the capacitor had leaked its "cooked" inards. A small scaping device managed to get most of the material off, the rest came off using a cotton bud.
- Solder in your replacement capacitor, making sure you get the alignment correct. Check that your solder connections are clean and complete.
- Reassemble the unit, reversing the disassembly process.
- Plug the unit into the mains power, and turn it on. Wait, then turn off the power. If all seems well (no loud bangs, puffs of smoke etc when you had the mains connected), reconnect the unit to your TV.
- Set your TV to the appropriate input, and turn the unit on. You'll need to go through the initial language selection, location selection and channel tuning process as with a new unit. Once that is done, use the remote to switch the unit to standby. If the replacement has been successful, the unit should go into standby.