Hello,
To begin with, for your safety, a warning: Please note that the internal circuits work with high voltages. All work inside a compact Mac (such as the SE) can be very dangerous, and must be performed be qualified personnel only. Dangerous charges can remain in various components even with the computer turned off and disconnected from the mains.
Old hard drives can sometimes suffer from a "stiction" problem. Normally, one would remove the hard drive and try to swing it, or knock on it, in an attempt to make the disk move. Without removing the hard drive, a temperature change may or may not make the drive work.
The Macintosh SE did not include a modem. There were external modems specifically for Macs. However, you can easily connect an old external (PC-style) serial dial-up modem to the MiniDIN-8 modem port. More or less anything between 9.6 kbps and 56 kbps will do; throughput is not going to be high anyway. The typical dial-up modem has a DB-25F port, so a normal Mac modem cable (MiniDIN-8M to DB-25M) can be used.
If you have access to two landline phone lines, you could connect the Windows 2000 laptop (which besides a DB-9M serial port may have an RJ-11 built-in dial-up modem port) and the Macintosh SE over the public telephone network.
Alternatively, it is possible to connect two modems locally, via a standard RJ-11 to RJ-11 phone cable. A simple line simulator (consisting of a 9 V battery, a 330 Ohm resistor, and a modified RJ-11 cable) may or may not be required in this case (do not use a line simulator for connections to the public telephone network).
For transfers modem-to-modem (or via a null-modem link), communications programs (terminal emulators) will be needed.
Finally, with a Macintosh SE, System 7, and a modem, one could per se connect to the Internet (I once did that with an SE with 2.5 MB of RAM), but there is not much practical use for it today. First of all, there are very few Internet providers with dial-up services. Secondly, a browser such as the old MacWeb, could not do anything with modern web pages. Old email clients will have a problem with authentication. FTP might still work.
So, look through the software available to you. Do not hesitate to post back with any questions.
https://support.apple.com/kb/sp191
https://everymac.com/systems/apple/mac_classic/specs/mac_se.html
http://www.nic.funet.fi/index/mac/info-mac/comm/_Terminal/
http://www.knubbelmac.de/