How can I install Linux on an old laptop without CD-ROM or bootable USB (have Windows installed)

The laptop might be able to boot from network (PXE). There are numerous tutorials out there how to set up the server environment to run a PXE server. In fact the most easy way (if you own another machine) is to run tftpd32 on a machine in a dedicated LAN (do not connect it to your home router as it will conflict with the DHCP server running on the router).

The setup of PXE boot environment and configuration of kernels depend on the distribution you would like to use. Doing a quick google I have found this which describes how to set up tftpd32 on Windows in order to install Ubuntu on a remote machine.