You need to get/make a real DOS boot disk, either on a floppy disk, or USB flash drive. (XP DOS mode, even from the BartPE "boot to DOS" function, is not actual DOS.)
I would suggest using a USB flash drive memory stick instead of a floppy. The bios files these days tend to exceed the capacity of a floppy. Same principle though. Just make a bootable flash drive. HP makes a nice utility or two that will format one with systems files so it will boot:
http://h20000.www2.hp.com/bizsupport/TechSupport/SoftwareDescription.jsp?swItem=MTX-UNITY-I23839
or
http://files.extremeoverclocking.com/file.php?f=197
I've successfully used the one linked by the second URL in Windows 7-32 bit but not the utility referenced in the first link since it won't install on the newer OSs. If necessary, find somebody who will let you do this on their XP machine or their Win 7-32 bit if it won't run on Win 7-64 bit. Note that you also have to download the Windows 98 system files referenced by the second link. The utility requires the old Windows 98 system files to make the flash drive bootable.
So here's an outline for using the utility referenced in the second link:
1. Plug in a USB flash drive of at least 2mb capacity (make sure you copy any important files you want to save into a folder on your hard drive as the formatting of the drive carried out as per the directions below will wipe out any files stored on the flash drive).
2. Download and install the HP USB bootable flash drive maker utility.
3. Download the Windows 98 system files and put them in a place on your computer's hard drive that you can refer to (a folder on the Desktop works nicely).
4. Run the utility which should now show up in Windows Start programs menu.
Run it as "Administrator" by right clicking on the program item in Start menu. Select the device you are formatting via the user interface and tell the utility where to find the Win98 system files when it asks you.
5.When the utility is through formating the USB flash drive and installing the system files, copy the DOS-based bios flash file to the USB flash drive.
6. Reboot the computer and make sure in bios you set the boot order to make the computer boot first off the USB flash drive.
7. When the computer has finished booting to the DOS prompt, type, "dir" and you will get a listing of the files on the USB flash drive. Visually locate the bios flash file you copied to the USB flash drive in 4. above. If the file name is longer than 8 characters you will see "~" in the string.
8. Type the part of the file name to the left of the .exe extension exactly as it appears on the screen, including the "~" if there is one. Hit the Enter key.
9. Wait for the flashing to proceed to completion. Don't restart the computer before it's done. It will take a minute or less I'm guessing.
10. Reboot into bios and set bios to default values, often done with the F9 key. If Windows was installed with the bios set to ACHI or RAID (as opposed to SATA or IDE) for the disk storage option you will need to make sure that one setting is not left at default or you won't be able to boot into Windows.
11. Boot into Windows.
12. Reboot and reset your bios options to the non default values you may have been using before flashing the bios.
Hope this helps.