Are you trying to install the whole software suite or just the driver? At the ATi site I see both downloads. Drivers & Tools | GAME.AMD.COM
If this is a recent problem, you could try doing a system restore to a point before this started happening. Info here if needed: System Restore - How to
Also you could open task manager (Ctrl+Shift+Esc). Go to processes tab and click on 'show processes for all users' (continue at UAC prompt if necessary). Then click on the CPU column header so the busiest processes will come to the top. Watch and see if you can determine which process is causing the spikes.
On a side note, if you go to User CP and click on edit system specs on the left, you can fill in as much info as you can and then we won't have to ask and you won't have to answer whenever you have a question.
Hope this helps. Please keep us posted.