The short answer, is yes, there are spacecraft you can "ping" (or do a non TCP/IP equivalent).
For two-way communications, implied by your desire to "ping" you should look at the amateur radio satellites. Many of these serve as packet repeaters. You need to be a licensed amateur radio operator, and have the right equipment, or course. A two-way UHF/VHF amateur station probably runs you in the \$5k to \$10k range. Of course, not all amateur satellites use UHF or VHF. For the ultimate satellite "ping" using an amateur radio station you can also bounce a signal off the moon.
One of the best known amateur satellites is AO-7. Satellite became non-operational in 1981 due to a battery failure, and then in 2002 came back to live as the battery went from a short to an open circuit. When active in sunlight (since it has no batteries) it has two repeater modes that are available to the public.
If a two-way station sounds too complicated, there are plenty of satellites that you can listen to with a simpler downlink-only station. SatNOGS is a particularly popular open-source network of ground stations, and their web site has great tutorials for getting started. You can even download images from US government weather satellites. This tutorial shows how it can be done with a software define radio and hand held antennas (investment < \$200)