WeAreBack just released the sourcecode for the WabModcheap - an application which lets you run your backups without installing a modchip. You can connect your Wii to your PC (using a selfmade cable) and then use the application to simulate a modchip!
Includes source code AND a Windows binary!

EDIT: Thanks Juan for finding this cheapmod.pdf (pdf)

EDIT: new video found for proof!

Modded Wii Using LPT Cable

Cable instructions:
WARNING: NOT NOOB FRIENDLY! If you cannot understand this, this is not for you!

In order to make the datacable, you need only a few basic items. A DB-25 connector, two diodes, and some cable. Connect the diodes in reverse (so, PC —|< --- Wii) to the DB-25 connector, to pins 1 and 14. Just connect some wires to pins 18 and 11, these will be the GND and output wires. The other two dioded wires are clock and input. Now, open your Wii, remove the DVD drive, and turn it over. Look for the following pattern near IC3001 (http://wiire.org/Wii/console/disc_drive):
- 1 -
2 3 4
- 5 6

3 is SBO1 (Output)
4 is SBT1 (CLK)
6 is SBI1 (Input)

With the numbers being pads, and - being nothing. Now, solder the wire from pin 1 to pad 4 (CLK line). Pin 14 goes to pad 6, and pin 11 goes to pad 3. Just find a suitable place to attach the wire from pin 18, which is GND. (Placing the board so you can read the writing on IC3001, look at connector P3001, the rightmost pad is GND and the third from the right is GND). Check your solder connections with a multimeter, then close up your Wii, and issue the ./dvdtool -r 0x8000 command in root mode. If you see hexadecimal numbers, congratulations! If you don't, check the proper functioning of your cable, wether or not you're in root mode, and if the parport0 and ppdev drivers are properly installed.

wabmodcheap-d2a.zip
wab-wii-d2b.zip