I tried to do an HP system recovery from boot but I got an error message "STOP: C000021a {Fatal System Error}
The Session Manager Initialization system process terminated unexpectedly with a status of 0xc0000013 (0x00000000 0x00000000)
The system has been shut down"

Hi there, if you can boot into Windows successfully could you not try it from there? I know this wont rule out the initial problem, but at least we can see if this method is successful.

I can boot into Windows fine but when I try to do a recovery from there it just shuts down and says Windows is shutting down but doesn't turn off or restart unless I do it manually.(by pulling the plug)

Whats the model of you HP Computer?

Presario SR1705UK (XP SP2)

Other errors occur during the recovery process
If there are bad areas on the hard drive, errors can occur during recovery. Scanning the disk drive for errors can isolate these bad areas, so they do not interfere with the reading and writing of files. If Windows does not open, run chkdsk from the recovery console.

NOTE: If you have a recovery tools CD or a Windows XP recovery console CD, open the chkdsk utility from the recovery console instead of using the Windows steps in this section. For more information on using recovery console, refer to HP and Compaq Desktop PCs - Using a Recovery Console to Resolve Startup Issues .

If you are still able to use Windows, perform the following steps:

1. If you are performing a recovery from a hard drive partition (pressing F10 at startup), skip this step.
   Remove and gently clean the surface of the disc using distilled water and a lint free cloth. Reinsert the disc and try again. If the error persists continue using these steps.
2. If you are performing a recovery from a hard drive partition (pressing F10 at startup), skip this step.
   Remove the disc and examine the disc for scratches. If the disc is scratched, you can attempt to repair the disc using an optical disc repair kit. These types of kits use special chemicals that bond to the surface of the disc and fill in the scratches. Disc repair kits may be purchased from major electronic stores or places that sell DVD movies. Once the disc has been repaired reinsert the disc and try again. If the error persists continue using these steps.
3. Start and My Computer.
4. Right-click the main hard drive (usually C and select Properties.
5. Click the Tools tab, click Check Now, and select Automatically fix file system errors and Scan for and attempt recovery of bad sectors.
6. Click Start and click Yes in the message window.
7. Restart the PC.
   The disk check starts after the initial startup screens and can take a very long time.
8. Retry the recovery process after disk scan has finished.

If I look at it with just what you gave us, and not what MadGamer posted (which I suggest you still follow, as an official HP source should at least narrow down what's going on), I have to think that something is interfering with the process starting successfully. Click the BSOD link in my signature, as the error you posted seems to be a stop error, and follow the instructions to posting the dump file.

From there we can continue searching for the cause, or maybe discover it from the dump. Who knows? I just have a gut feeling that this crash dump is just going to be redundant, but I still want to see it.

Also, if there's any way you can make System Recovery work without booting to Windows (I.E. a Recovery Partition or a CD HP sent that you can boot from), use that.

P.S. There's always a chance we can solve what happened without you needing to do a System Recovery, so perhaps you should post that problem too.