Computer shuts down when on the Internet

We have two computers that turn off after going on the Internet. We are running Windows XP, all updates are current, as are BIOS, Antivirus, video drivers are current. We have several of these models but only these two shut down. They are IBM ThnikPad A21m. Both have passed PC-Check diagnostics. Have replaced memory and DVD drives just as a precaution. They still shut down.