i have laptop hcl k38.how can i install 16GB ram in laptop.

HCL Leaptop K38-MTV?
I found this site: http://www.india-server.com/laptops/features/hcl-leaptop-k38-mtv-30.html
It says 8GB is max.

if my laptop doesn`t have ram installed inside can the laptop switch on?

If you turn on a laptop without RAM modules installed, you’ll get one of the following:
1. The laptop will turn on but the screen will stay black.
2. The laptop will turn on and start beeping.
3. The laptop will turn on and after a while turn off.

Can I install a hard drive that has been cloned from a T52 2888 then update it from Lenovo’s website with the T42p drivers

I don’t know. You’ll have to try because it might work. I’ve done it before a few times.

if I can’t use the data on this HDD how do I wipe out the T52 data on the cloned HDD to use it or when I load the the new OS it will be done automatically.

You may choose to repartition and reformat the hard drive while installing Windows from scratch.

I was given a IBM Thinkpad T42p 2373, this laptop has no ram installed in it, in the bottom slot or the slot under the keyboard. I have 1 stick of 512 PC2700 sodimm out of a T51, my question is can I install it in the bottom slot or do I have to install it in the slot under the keyboard for the laptop to work? I’m only going to install one dimm since I only have one.

You can use either slot.

I was able to get into the BIOS, but it won,t start in safe mode or any other option. Won’t boot from the cd, so I tried reinstalling the OS, not reformatting it, [I'm trying to save my data]. that didn’t work either. I got a BSOD though. Could this mean that I need more RAM?

I don’t think so. When your laptop doesn’t have enough RAM it slows down, but should get any BSOD error.
It’s possible that you have a hardware related problem.
You have two memory modules installed into the laptop, right? Can you remove them one by one and test the laptop with each module separately. Can you boot the laptop when only one of the modules is installed? If you can, most likely the other module is bad.
If your laptop fails to boot with either module installed, apparently it’s not memory related issue. It’s very unlikely that both memory modules fail at the same time.

Try removing them one by one first.