I have bought a new HDD for installing a new operating system. Can I, in case I'm missing files, attach the old TrueCrypt-encrypted hard disk to USB and mount it in TrueCrypt?
Or doesn't this work for system-encrypted hard disks?
In the TrueCrypt GUI, choose the partion of the external drive, then select "Mount without Pre-Boot authentication" from the Tools menu.
This will let you mount the volume as if it were an encrypted device without the boot loader (the difference just being a few offsets as to where TrueCrypt should attempt to decrypt the volume header from)
I don't think the system encryption feature of TrueCrypt binds to the other hardware.
You will need the TrueCrypt boot loader engaged in the boot process to unlock the system encryption on that drive. The TrueCrypt Rescue Disk might be useful for this.
However, there is always the option of booting from that drive and removing encryption (which works in place) before using it this way -- could take some time depending on the drive size.