The problem is that the current installation of the OS (I'm assuming Windows) will have the drivers for the particular mobo chipset and graphics card you currently have.
If you simply plug the drive into the new mobo it won't work properly - if at all - until you install the correct drivers.
It might be possible to start the system and load the correct drivers, but it just as likely won't.
Now if you have the correct installation CD / DVD for your OS, you may be able to "repair" the installation and load the correct drivers, but this is not guaranteed, and can be further complicated by the original CD / DVD being a lower Service Pack version than the installed version of Windows.
The simplest approach would be to get a new hard disk - preferably a bigger, faster SATA disk - and install your existing as a second / slave (apparently we aren't supposed to say slave anymore - PC gone mad) disk. However, you will have to re-install your applications, although your data would remain untouched.
Whatever your approach, ensure that you have a full backup before you start. If you can't backup the disk, don't use it.
An alternative is to find out what your current problem is and see if you can fix it. It might be a relatively simple fix - faulty RAM, unseated RAM or card, etc.
SD