You should have given your son access to a Parental Controlled Account only. Unfortunately without the disks, and from the sounds of it, no backup, you are stuck. You might be able to recover the information with an external hard drive and an appropriate data recovery program, but getting the 10.4 original discs is increasingly difficult. If a Mac is Intel, only the original discs can be used to install 10.4 which you would need to call AppleCare for and hope they still have a copy of, or a cloned backup. If it is PowerPC G3, G4, or G5, you can probably find the 10.4.6 retail disc, discussed here to Archive and install 10.4.
Before Archive and Installing, which you can do with either the original 10.4 or retail disc, be sure to attempt that data recovery. If you choose to try to Archive and Install 10.5, and you have PowerPC, you'll lose access to Classic Applications. You could upgrade to 10.6 if you have Intel and 1 GB of RAM, or 10.7 if you have 2 GB of RAM, but some application compatibility might be lost the further you upgrade.