If you have the i7-860, then the maximun performance difference you'll get is just over 10%, from the i7-880, that's far from being a good upgrade. Your CPU is still a decent one, faster than some budget CPUs.
I'm not sure how much of an upgrade the extra HDD would be in terms of performance, if you could move your OS installation and programs to the new drive, then it would be a good upgrade, a new 128GB SSD is probably the way to go if you could reinstall windows, i wouldn't buy a HDD unless you're running out of space on your current one.
Do the pc have a sticker or something else, that shows the windows product key? (I assume it runs windows) If you have that key, you might be able to reinstall windows on a new HDD or SSD
For the speed of your current HDD, if it's 4 years old, then you should do a defragmentation of the drive, it's going to take some time for it to do it, though it should tidy up the HDD, making it faster. Over time the drive will write and delete files when you're using your pc, this leaves the files kind of scattered around on the drive so it's harder to find, defragmentation will collect all of these pieces together, making the files easier to find.