I am running Red hat on a virtual box. My current kernel version is 2.6.18-155.el5.when I install the new kernel 2.6.35.4, I do not get any error during the install but the kernel fails to boot. I get the following error.

mount: could not find filesystem '/dev/root'
setuproot: moving /dev failed: no such file or directory
setuproot: error mounting /proc: no such file or directory
setuproot: error mounting/sys: no such file or directory
switchroot: mount failed:no such file or directory
kernel panic-not syncing:attempting to kill init!

I am new to Linux. Can anyone help me out here.

Redhat puts a lot of effort into packaging their RHEL systems - that's why people pay for it.
It's also licensed, which means you can't (legitimately) just copy it.
So ...

What are you trying to learn/achieve - maybe we can offer a solution.

I am using this for a course on Linux device drivers which requires installation of the kernel's latest version and all module programming to be done on the newly installed kernel. I am currently working on 2.6.18-155-el5. I downloaded and installed version 2.6.35.4 and when I try to boot this version I get the error which I have mentioned above.

I wouldn't have thought RHEL was the place to do this.
Where did you get the .config from ?. If it's from the RH environment, you'll need to build an initrd to ensure the required support to mount the root is included. I build all that into the kernel itself when I build one so initrd isn't an issue.
Have a look at the CentOS (the open source equivalent to RHEL) wiki for doco on how to do all required.

A pretty generic approach:

Your error is: mount: could not find filesystem '/dev/root'

There can be 2 reasons: either the disk device drivers are not found, which is plausible in virtualization land, or the filesystem device driver is not found;
I bet the 1st one is the case, although I've erred years in the past forgetting to build in support for ext2 (at that time)

Your steps would be:
1st: identify the filesystem type (ext4, reiserfs, ...) and disk type (ide, virtio, scsi, ...)
2nd: check if support is available in the kernel for either, and you have it compiled in (if not, enable it and recompile your kernel)

In the case of a virtio disk type, you may have to make an initrd with at least the modules virtio, virtio_blk and virtio_pci. (maybe more, doing this from the top of my head)

You may have to run some setup commands for your bootloader to recognize your initrd (if you have one) and kernel.