Hi UndeadMage and welcome to TSF!
OK, one thing is setting warning bells going here, that second stop code 0x24 - that means the file which allows you to read from and write to NTFS file systems is corrupt (ntfs.sys), normally because of file system corruption or disk problems. If possible, go to your hard drive manufacturer's website (on another computer as I believe you said that one has no net access) and download their disk checking utility. You'll probably need to put this on a floppy disk, but you may be able to make a bootable CD to run it. Run a full scan on the disk and see what it picks up. If it picks up errors on the disk, you're going to need to get another hard drive as this one is dying.
Also, this tool will allow you to do a zero-fill on the drive. If the disk scan turns up nothing, do the zero fill (note, this is sometimes called a low level format by some people, and it will irrecoverably destroy any data left on the drive) and try a re-install of your OS. If you're still getting errors, post back and we'll see what we can do.
You say you "bypass[ed] the safety thing that hinders diskette formatting" - are you talking about the little tab on the diskette? If so, stick a bit of paper over the hole with sellotape and you can write to it again.
One final thing to note, if you're installing XP on this system, are you using the same licence as the one on your new computer? If so, you're technically in violation of the licence agreement - Microsoft only allow you to install a copy of XP on one computer, and if you're putting it on another you need to completely remove it from the old system first.
OK, one thing is setting warning bells going here, that second stop code 0x24 - that means the file which allows you to read from and write to NTFS file systems is corrupt (ntfs.sys), normally because of file system corruption or disk problems. If possible, go to your hard drive manufacturer's website (on another computer as I believe you said that one has no net access) and download their disk checking utility. You'll probably need to put this on a floppy disk, but you may be able to make a bootable CD to run it. Run a full scan on the disk and see what it picks up. If it picks up errors on the disk, you're going to need to get another hard drive as this one is dying.
Also, this tool will allow you to do a zero-fill on the drive. If the disk scan turns up nothing, do the zero fill (note, this is sometimes called a low level format by some people, and it will irrecoverably destroy any data left on the drive) and try a re-install of your OS. If you're still getting errors, post back and we'll see what we can do.
You say you "bypass[ed] the safety thing that hinders diskette formatting" - are you talking about the little tab on the diskette? If so, stick a bit of paper over the hole with sellotape and you can write to it again.
One final thing to note, if you're installing XP on this system, are you using the same licence as the one on your new computer? If so, you're technically in violation of the licence agreement - Microsoft only allow you to install a copy of XP on one computer, and if you're putting it on another you need to completely remove it from the old system first.
