If it is remember that the processor may already be damaged. Monitors that don't work once they have warmed up a bit. The best way of overcoming this is to ensure that you have a fresh and clean installation of the operating system. You'll find it makes life a lot easier to do this before you start using the computer than after six months of use. Ask to see the receipts anyway.
Many laptops offered for sale as used machines are actually stolen machines.
Other Tips Make sure you get all driver disks with the computer. Make sure also that you have drivers for the Windows 95 or Windows 98 that you intend running on that computer. Ensure that you have a clean hard disk. You want to erase any software or user files that the previous owner had on it. Get a copy of every piece of software sold you with the computer.