Internet recovery -2002f error

I have an iMac late 2013 series model A1418 (EMC 2638). I can't find out the operating sytem version without booting into MacOS, so I post it to this category.

The computer recently began to display a flashing exclamation point at startup, so I booted with Option key pressed and it offered internet recovery. After I click “internet recovery” it asks to choose a connection. However, after entering a correct password it either gets stuck with globe spinning for hours or displays a -2002f error after a while.

If you connect the computer with an Ethernet cable to the router it still asks for a Wi-Fi connection, and if you do not enter its credentials nothing happens for hours.

A Windows 8.1 laptop uses the Internet without problems both over Wi-Fi and Ethernet (with corresponding cable plugged into the same port of the router).

The router (TP-Link TL-WR840N) assigns dynamic IP addresses 192.168.0.x, with subnet-mask 255.255.255.0 and default gateway, DHCP-server and DNS-server all 192.168.0.1. So it is as simple as it can be.

Connecting the iMac to the internet provider directly – over Ethernet without router – does not help either. However, the provider requires a fixed IP address (10.180.21.76), 255.255.252.0 subnet mask and its own DNS server (192.168.248.21). So iMac may not be able to use this connection due to non-standard settings (you can't change the parameters).

Unfortunately, I have not made a boot disk previously.

Please let me know what other options I can try.

Thank you.