First, you may consider getting a standalone monitor and plug it into the back or side of the laptop. Most laptops have a vga plug built into them to run a external monitor. Many people opt to do this since the parts alone for replacing the original monitor are so expensive and it is extremely hard to find a technician to replace the components that need to be replaced.
Second, since most of the time it is cheaper to purchase a laptop that is exactly like the one you have than purchasing the replacement components for the monitor, you can purchase an exact laptop and swap out the hard drive that holds all your personal information.
Third, you can purchase a new laptop and clone the broken computer with cloning software and then install the clone program on the new computer. By doing this it will make your computer just like the broken one as long as you purchase one just like you presently have.
There is no real simple solution for fixing a broken monitor on a laptop. This is one of the most fragile parts of a laptop also. There are many parts to a monitor and to replace them you almost need to be a surgeon, this is why it is so hard to find a computer technician to work on them. I hope that you do not have to be bothered with this problem and your monitor never gives you a problem.