I had RH9 with kernel 2.4.whatever. I downloaded the 2.6.1 kernel in an rpm from the Fedora proj. site, and ran "rpm -Uvh filename.x.x.x.rpm". It ran with almost no errors, the errors being module independencies which I fixed. When it was done, I rebooted, and got the following, with lines that may be important in bold:

ERROR: /bin/insmod exited abnormally!
Mounting /proc filesystem
Creating block devices
Creating root device
Mounting root filesystem
mount: error 19 mounting ext3
pivotroot: pivot_root(/sysroot,/sysroot/initrd) failed: 2
umount /initrd/proc failed: 2
Freeing unused kernel memory: 236k freed
Kernel panic: No init found. Try passing init= option to kernel.

You should have done rpm -ivh, that would have installed the 2.6 kernel and leave the 2.4 untouched as a fallback. There is a doc somewhere on the Red Hat site about upgrading kernels, which is linked to on every errata page concerning the kernel.

However, the 2.4 modutils (like insmod) don't work with the new kernel.

Untested suggestion:
Get the latest modutils package (for 2.6 now called module-init-tools - at least in Debian).
Boot a rescue system, mount your hd partition(s), do a chroot and install the package with rpm.

You probably have a kernel built with initrd support.
Create an initrd for the 2.6 kernel with mkinitrd.
Pass the initrd = XXX after the kernel = XXX line.

The 2.6 kernels use a new module format which requires you to update your modutils package as ricstirato said. Your old modutils should still remain on your system as modprobe.old, depmod.old and so on, so you can still run your old 2.4 kernels. I ran into this exact same problem when I compiled the 2.6 test kernels. HTH :-)