Lost Windows XP disks

Hello,

I have an Acer stack system, that had windows XP home basic installed on it.
When i purchased the computer i made recovery discs as required.But unfortunately when I moved home, i lost the recovery discs and did not find out until i had a major problem with the operating system.

I could not get the system to run, but every time i looked through the drive i found that the files and folders were disappearing.
I thought the only thing that could be causing this was a virus, so with the advice of a friend i had to format my hard drive.

But silly me i forgot to look out the recovery discs first, and found that i had lost them after i formatted the drive.
As i am a complete novice i thought that as when i purchased the computer, then i must have purchased the operating system.
But to my surprise i had only purchased a copy as it was pre installed.

Now i have been told that if i get a loan of a copy of windows XP, and install it on my machine, but use the product key i have on my computer then all will be OK.

Is there any truth in this?.

I would be most grateful for any advice you can give me on this problem, I do not want to pay Acer another £50 just to get my pc going again.

Thank you
Steve .