Last update
Sad news... But according to gc-linux.org, not all features/drivers currently implemented into mainline kernels:
gc-linux.org wrote:
"Note though that most driver support is still missing in mainline"
So, if you want to use most features, you still need to use 2.6.32 with mikep5 patch.
liquitt wrote:So, today we tried building 2.6.39 and 3.0.4 Kernels ... without success.
Not very informative, what errors you get? What cross compiler you used?
root@s666otrs001:/home/gclinux/linux-2.6.39# bzip2 -cd <../mikep5-patch-2.6.32-gc.bz2 | patch -p1
Not so good idea

Btw, if im not wrong - Linux kernels with odd number versions (39, in this case) are historically means to be "unstable". (even number version - "stable") It may nothing to do with your unsuccessfull compile, of course.
Would be nice to see some work or information on this.
Will right now try to compile 2.6.38, with compiler from my guide

Will update this post with results.
update
Successfull compile

Used cross compiler from my guide. 2.6.38 with default config, no patches.
Code: Select all
$ tar xjf linux-2.6.38.tar.bz2
$ cp linux-2.6.38/arch/powerpc/configs/gamecube_defconfig linux-2.6.38/.config
$ make -C linux-2.6.38 ARCH=powerpc CROSS32_COMPILE=powerpc-linux-gnu- CROSS_COMPILE=powerpc-linux-gnu- menuconfig
(just take a look, nothing changed, then exit)
$ make -C linux-2.6.38 ARCH=powerpc CROSS32_COMPILE=powerpc-linux-gnu- CROSS_COMPILE=powerpc-linux-gnu- zImage
...skip....
BOOTCC arch/powerpc/boot/cuboot-sam440ep.o
BOOTCC arch/powerpc/boot/cuboot-acadia.o
BOOTCC arch/powerpc/boot/cuboot-amigaone.o
BOOTCC arch/powerpc/boot/cuboot-kilauea.o
BOOTAS arch/powerpc/boot/gamecube-head.o
BOOTCC arch/powerpc/boot/gamecube.o
BOOTAS arch/powerpc/boot/wii-head.o
BOOTCC arch/powerpc/boot/wii.o
BOOTCC arch/powerpc/boot/treeboot-iss4xx.o
BOOTCC arch/powerpc/boot/empty.o
HOSTCC arch/powerpc/boot/addnote
HOSTCC arch/powerpc/boot/hack-coff
HOSTCC arch/powerpc/boot/mktree
DTC arch/powerpc/boot/gamecube.dtb
DTC: dts->dtb on file "arch/powerpc/boot/dts/gamecube.dts"
WRAP arch/powerpc/boot/dtbImage.gamecube
rm arch/powerpc/boot/gamecube.dtb
make: Leaving directory `/tmp/ramdisk/linux-2.6.38'
$ file linux-2.6.38/arch/powerpc/boot/zImage
linux-2.6.38/arch/powerpc/boot/zImage: ELF 32-bit MSB executable, PowerPC or cisco 4500, version 1 (SYSV), statically linked, with unknown capability 0x41000000 = 0xf676e75, not stripped
$ powerpc-linux-gnu-gcc -v
Using built-in specs.
Target: powerpc-linux-gnu
Configured with: ../gcc-4.3.2/configure --target=powerpc-linux-gnu --prefix=/tmp/ramdisk/gc-cross --enable-languages=c --disable-nls --without-headers
Thread model: posix
gcc version 4.3.2 (GCC)
$ powerpc-linux-gnu-as -V
GNU assembler version 2.18 (powerpc-linux-gnu) using BFD version (GNU Binutils) 2.18
I didnt tried to boot it on gc, because it need to be configured, as default config even didnt use framebuffer console. It was just a compilation check.
Did you used crosstools from my guide? Are you sure that compilation of tools itself went ok?
About this
sed command in my guide - i used it specifically for my linux system, because configure script of binutils-2.18 conflicts with some newer version tools i use on my linux-box. Maybe you catch some problem like this - and didnt get tools compiled at all?
update 2 
Downloaded 2.6.39 kernel. Same cross tools, default config, no changes , no patches - same result, no errors and freshly builded zImage.
update 3
Not a good news. Tried to boot 2.6.39 on gc. But at the first, i wanted to recompile kernel to enable framebuffer console - when i get in config, i didnt find wii/gc videointerface. I search entire sourcetree, and there is no such device

Checked gc-linux.org and the bad things come true - yes, they started to implement gamecube support into mainline kernel, but not all features currently implemented. So seems, that video part is one of them.
So, if you want to have most features you need to use 2.6.32 with mikep5 patch.