Trouble shooting an install with no display is always very difficult.
However what we realistically need to determine is if the machine is booting or not.
If at all possible can you connect this machine to a local network once it's booted, then find some way of polling the network to see if anything new shows up. You can do this with another linux based machine and tools such as Nmap.
Alternatively, if you have access to another machine, and it has a serial port on, and you can get hold of a serial to serial cable try connecting the two machines and see if anything appears on the serial port.
Most *nix based Operating Systems (Ubuntu included) will in most cases make a terminal available on serial port if one is detected at boot up.
If you fire up a serial terminal on the working machine and get a login prompt from the other machine you know your booting ok, and the issue is likely a graphics driver and / or display resolution out of range problem.
Another thing you can also try is pressing various combinations of ctrl+fkey or ctrl+alt+fkey In most cases this will drop you to a command line and providing your install is not trying to set a strange console resolution from the boot you may actually get something usable.
UPDATE FOLLOWING OP's addition of comment stating removal of hard drive
I can only assume that you booted from a Live distro CD, in which case it sounds to me like the primary partition on your first hard drive is not marked as bootable.
If this is the case, you need to do 2 things as follows:
1) Put the internal hard drive back in, then using the laptops BIOS configuration, set the boot priority of the machine to boot first from CD/DVD then from the first hard disk. To get into your BIOS there will be some message on your post screen that states press XXXX to enter setup. XXXX is often the del key, or F1, F2 so on.
2) Use the disk partitioning tools on the live CD (You'll most likely need to be in rescue mode) and set the first partition on your hard disk to be bootable.
IF all is ok and there is a working OS on that drive, then you should hopefully see it start to boot, if it tries to start from CD/DVD then remove the disk from the drive and try again, or use your BIOS as previously described to change the boot order back to hard drive first.
IF the primary hard drive partition is already marked bootable, then chances are your hard drive has a damaged first few sectors. Now this is not as bad as it sounds, you can sometimes if your lucky manage to partition around it, but you need to start getting very creative with your partitioning tool if your going to do this, it's not a job for the feint of heart.