Set has a problem:
Computer won't turn on.
Computers usually give out a "beep code", number and lenght of beeps indicating the type of the failure. In case of receiving this beep code, you may interpret it using as guide this webpage:
So, using a CD resident OS looks useless.
If you are not getting any beep, there are two options:
1. It's a problem with your hard drive
2. It's really a serious hardware problem
As I saw in your previous question, you already tested with a new hard drive, so the first option is discarded.
You can try pressing F8, in some computers you can access and modify boot sequence. Test, what happens
If you could boot up, you should try to get a CD resident OS (might be Windows, Linux, DOS etc) with diagnostics and repair applications. I won't extend about this point bacuse I'm quite sure you can't boot.
So, if nothing happened and you still can't boot you may check is you have a problem with the memory. You can open your computer and remove memories, replacing one by one because it might be a bad memory conflicting with the rest. You should do this just to test if it starts up. You should have no problem to start up with, let's say 512 Mb.
See how to open your laptop and search for the memory here
or do a google search for your proper Lemovo model. If you don't feel you can mess with the interiors of your laptop, better don't do this; ask for help from someone more experimented.
If you still have no luck, no beeps, no access to bios, no way to start up with an external drive and no results checking memories, I'm really sorry, but my only reminding advice is to take is to a computer repair service.