I would suggest just to change the hard drive and not going for a new computer as long as this one works fine (my Desktop is from 2005 too :-) ).
As an example, since I got my first computer with a Hard disk back in 1993, *all* my computers' original hard disks failed on a given time and had to be replaced. This makes a total of 4 desktop PCs and 3 laptops with hard disk failure.
That is to say mechanical hard disk failure is quite common and they are easy to replace...
In order to avoid re-installing your OS, I would suggest to use Clonezilla which can make a full copy of your system on a removable disk then copy the whole to the new hard disk. Easiest is to install Clonezilla on a FAT-32 USB stick using Tuxboot, ensure you can boot from a USB stick first (to be enabled in the BIOS) and make sure you have an external drive (easiest would be a USB removable drive) to store the OS images. Takes just a few minutes to copy the OS on the new disk.