What game? I haven't heard of one yet that doesn't work with a "modded" Wii.
Anyway, turning off anything while something is installing is a TERRIBLE idea. Unless you have BootMii/boot2, you have no hope of recovery without a NAND programmer (requires opening the Wii, desoldering the NAND chip, soldering it to a NAND programmer (which you'd have to buy), reprogramming it via PC, then soldering it back into Wii. Only for people who are skilled at soldering, and know a fair bit about electronics.)