Unable to change password.

Since you seem to be having problems using traditional methods, here is an unorthodox method.
Password Reset
There is a listing at the bottom of the page that shows our tuts that use more traditional methods

I think that message indicates the computer and user account is part of a domain network. You could try this to enable the built-in local administrator account, and when logged in to that account you can create a new local admin account and set the username to whatever you want. That new account should hopefully then not have any restrictions.
Built-in Administrator Account - Enable or Disable

To log on with or without the username, see this: Log On with User Name and Password

Your best bet is to restore the computer to it's Factory New state. Found this:
4th post in this thread: How to restore acer laptop to factory settings without cd - Security - Windows Vista

Laptops from mid 2007 onwards dont have a recovery disc supplied with a purchase of a laptop. Instead, manufacturers added a hidden partion on the hard drive which contains the same files on a recovery cd / dvd.

To reinstall your laptop to the factory settings / "out of the box" settings, please follow these steps. It worked for me, and should work for you.

ALL DATA WILL BE ERASED ON YOUR HARD DRIVE IF YOU PROCEED. YOU WILL NEED TO ENSURE THAT YOU HAVE THE POWER ADAPTER PLUGGED IN. DO NOT SWITCH OFF OR RESTART YOUR COMPUTER DURING THIS PROCESS.


1) Hold down the power button for 10 (ten) seconds to switch off your machine.

Please note: Holding down the power button on the machine forces it to switch off. Any unsaved data will be lost.

2) Press and hold the 0 (zero) key and at the same time, tap the power button once to switch on your notebook.

3) When the machine Starts beeping; release the 0 key.

4) When prompted by the warning screen; select Yes to continue with the system recovery.

5) Select Recovery of Factory Default Software; click Next.

6) Select Recover to out-of-box state. Click Next again.

7) Click Next to Start recovery.

Setup a new account during the recovery process. Make sure to install all Windows Updates, including Service Pack 1 once the recovery completes.

Not knowing the age of your daughter and from whom the computer came from and what is on the computer I would recommend a Clean Install using the COA key on the Microsoft sticker.

Tutorial by Brink:

Clean Install Windows 7

My thanks to those who have replied to my question.
With my lack of computing knowledge I am very reluctant to modify the Registry and doing a clean install seems a bit drastic just to change a password. If these turn out to be the only workable methods to change a logon password I'm afraid my daughter will have to endure the one the notebook came with.
I did go into Option 1 suggested by Tookeri 'Enabling built in Administrator in Local Users and Groups' and found a Domain address under the 'Full Name' heading. The 'Password never expires' was the only box checked. I unchecked it and checked 'User must change password at next logon'. The "Apply" box did not seem to be highlighted but I clicked it, as well as "OK". I then closed down and logged off and back on. I had to log in with the existing password which I then attempted to change by the regular route. The new password was not accepted.
Perhaps I should first try disabling the built in Administrator account but I fear if I do I won't be able to log back on once I have logged off. Any further advice please?

Was the account you're talking about "Administrator"? The one with a domain address under the 'Full Name' heading
If not, was there an "Administrator" account?

Also, to be sure if it's a domain account or not, does the log on screen show the domain name and a \ before the user name instead of just the username? Example: domainname\username instead of just username

I meant that you should enable the local built-in Administrator account and log in to that. It may require you to click "Switch user" or something in the log on screen to be able to switch from domain to a local account which is usually shown as the computer name. Or try this trick: How to Login with a Local Account instead of Domain Account

And then create a new account of type administrator and name it exactly what you want. Then after that only log on with that new account and not the domain account.

Not sure why you are reluctant to restore the laptop to it's factory new state, especially since it's new to your daughter.

Seems to me she would be better off to start with what would in effect be a new laptop after the recovery completed.

That way she could setup her own userid and password and not have anything left over from the doner.

I agree with Ztruker, doing a factory restore is a better option. If you do that you will probably also never run into issues like this again, that you can't even change your own password. And who knows if there are other restrictions as well.

I think I can answer for all of us here that help people daily: If we were given a second hand PC to us, a clean install or at least a factory restore is the first thing we would do on that computer. A factory restore is supposed to be easy so anyone can do it. Personally I wouldn't want to use a computer that someone else has installed and put things on. They could have installed questionable programs and tweaked the system so you'll end up with problems one day.
With perhaps one exception: if I trust the doner to 100%

That was my concern in post #5.
When giving a used computer to a child a clean install would make sure their are not things on the computer a child shouldn't have, plus the bloat ware is gone.
If one has the COA sticker on the computer the clean install is free.