I have a desktop with a lot of installed programs and things that I don't want to lose. Even backing up can be a pain and some data may still be lost.
I was wondering if it is possible to upgrade the existing computer parts such as the Motherboard, RAM, CPU , Power supply and Case without changing the internal hardrive so I would ideally keep everything I have, it'd just be faster.
If so, is there a shop in Melbourne that would do this for a reasonable fee?
Yes you can.
Be aware though, that you will need to start over with a fresh install of Windows if you upgrade your motherboard, since the copy of Windows you have installed has drivers installed for the old motherboard. Without a fresh reinstall, it'll bluescreen or not boot at all since the chipset is now completely different.