Does the Catalyst 2940 acquire an address via DHCP? At least my DHCP
server doesn't show any address which has been requested recently.
This is possible, yes. However, per the answer by Teun Vink and others, by default a Cisco switch does not have an IP address configured (or may have an old/incorrect address). In order to assign a correct one, you may wish to check Chapter 4 of the Cisco Systems, Inc. Catalyst 2940 Switch Software Configuration Guide, 12.1(19)EA1. Here is an html version.
Per the manual:
You can assign IP information through the switch Express Setup
program, through a Dynamic Host Configuration Protocol (DHCP) server,
or manually by using the command-line interface (CLI).
[...] Use the switch Express Setup program if you are a new user and want to provide specific IP information. With this program, you can also configure a default gateway and an enable secret password.
Note: If you are using DHCP, do not respond to any of the questions in
the setup program until the switch receives the dynamically-assigned
IP address and reads the configuration file. [...] Use the manual method of configuration if you are an experienced user familiar with the switch configuration steps; otherwise, use the setup program described earlier.