The answer is MAYBE - how's that for encouragement?
The devil is in the details. All your files on the HDD WILL be there and can be accessed and used. The problem entirely is in the Operating System you have installed - probably Windows of some variety.
You see, when Windows is first installed on any machine, one important function of the Install process is to survey the entire set of hardware it finds itself working with and identify and install all the software driver files for all the various hardware devices. The "devices" are not just the cards you plug into the PCI bus. There are MANY devices that are part of the mobo - things like SATA HDD controllers, optical drive controllers, modems, audio chips, USB ports, etc., etc. All the drivers required for the devices on your old existing mobo were installed on your C: drive as part of Windows, making that version a customized version. This is always done for every Windows Installation.
Now, if you change to a different mobo, even if you then install on it ALL the extra parts your old system has, the new mobo itself has a whole bunch of new devices, and does NOT have some of the old mobo's devices. So when you try to boot up the first time, Windows loads all the drivers it has - for the OLD mobo - and tries to run. But it has the WRONG device drivers now! What happens? Well, usually something fails. If you're lucky it sort of works, but often it does not.
How to fix this? Well, the obvious option is you start from scratch and Install Windows all over again, BUT that normally means losing all your old data! Not a good option IF you can avoid it. But you might have to SO ... you REALLY should be making a complete backup of your old HDD so that you can recover files from the backup if that becomes necessary. Recognize, also, that ALL the application software you have installed already would need to be RE-installed if you have to re-install Windows first.
BUT there is another process that may work for you. When you FIRST start up the system with the new mobo installed, you should have your original Windows Install CD in the optical drive. You should use the right key during the initial boot to go into BIOS Setup right away. Check that everything looks OK, but make SURE you go set the Boot Priority Sequence this way: try the optical drive first, THEN the HDD. SAVE and EXIT and the machine will boot from the Install CD, not from the HDD. Do NOT do a normal Install. Look for the option to do a process called REPAIR INSTALL or something like it. This will try to re-do the process of customizing the device drivers. It will survey the hardware present and compare that to the device drivers already installed on the HDD. It will try to remove unneeded ones and add new ones that are needed for the new mobo. When it is finished, if it works properly, your machine should be able to boot and run normally from your OLD HDD, with all your apps and data intact! That is what you want, of course.
Sometimes this Repair Install process works perfectly. Sometimes it fails badly, especially if there are HUGE changes in hardware. Sometimes it works well, but leaves you with one or two devices not working. They show up in Windows' Device Manager with yellow Caution symbols on them. If that happens, you need to seek out the proper up-to-date driver for that device and install it yourself. It could be on the CD that comes with your new mobo, or maybe from the website of a part maker.
Good Luck! And really, even if you have to temporarily borrow a HDD from somewhere, MAKE a backup of all your current drive (an actual clone is a complete backup) and set it aside in case something goes wrong and you have to recover data. Or even, if it's really bad, revert to old hardware and completely restore your old HDD to get it working.