NASA sends presupply missions ahead of the Ares missions which are tracked by NASA the entire time to ensure they arrived intact. Why didn't Watney try to salvage a radio from one of those presupply probes?
In order to establish communications with Earth, Watney needed something with sufficient power and bandwidth to allow a reasonable data flow, and something that could send and receive a signal carrying that data.
A presupply lander would be little more than a shipping container with a parachute and/or inflatable cushions. No thrusters, no engines. They would be delivered into Mars orbit by a rocket, but would detach from the rocket to land somewhere near the planned manned landing site. They would be fitted with a simple low-power locator beacon that would allow astronauts to find the modules near their landing and base sites. There are a couple of reasons for this - the simpler something is, the less potential points of failure; and the simpler something is, the less mass it adds to the payload (and therefore, the less fuel needed to get the payload from Earth to Mars).
Pathfinder was the closest thing that Watney knew the location of that had reasonably high data-capacity for two-way communications. He was able to use hexadecimal to allow NASA/JPL to position the rover's head and communicate that way (obviously, he could write plaintext on his whiteboard/cardboard and have the camera send back the image - allowing a much higher throughput from Mars).
We later see NASA/JPL provide instructions for Watney to connect Pathfinder to his rover to allow them to send higher capacity textfiles, and he was able to reply in kind.
NASA sends presupply missions ahead of the Ares missions which are tracked by NASA the entire time to ensure they arrived intact.
These 'presupply missions' were definitely capable of two-way communication. While not necessarily video and/or audio capable, at a minimum the unmanned supply vehicles would have to be able to report their positions during the trip to Mars and receive course corrections from NASA's mission control. IRL, NASA was able to troubleshoot the New Horizons Pluto probe at a distance of 3 billion miles with a nine hour two way communication time (source). Sending and receiving messages to an unmanned Mars supply lander within a time window governed by Mars' rotation and possibly utilizing one or more communication relay satellites orbiting Mars seems entirely plausible.
Additionally, the MAV (Mars Ascent Vehicle) may have been the only 'unmanned supply vehicle' already present at the Ares 4 site, it isn't clear whether any of the other unmanned supply missions have even been sent yet. While the MAV may have gone to Mars unmanned, it was expected to return the Ares 4 crew to orbit and rendezvous with the main space vehicle. That's something that is going to have a wide spectrum of two-way communication. Here are some excerpts from the script (source).
TEDDY SANDERS: You’re not the only one who needs satellite time. We’ve got the Ares 4 supply missions coming up. We should be focusing on the Schiaparelli Crater.
MARK WATNEY: Every Ares mission requires three years of pre-supplies. So NASA decided a long time ago it's a lot easier... to send some of the stuff beforehand rather than bring it with us. So, as a result, the MAV for Ares 4... is already there at the Schiaparelli Crater, just waiting. So the plan is for me to use that to go into orbit... just as the Hermes is passing... and I guess they catch me?
Why didn't Watney try to salvage a radio from one of those presupply probes?
In universe, the only logical explanation is that the Ares 4 site at Schiaparelli crater was simply too far to reach geographically at the time. The Pathfinder site was vastly more accessible and good practise to field test the rover.
Watney takes the rover to retrieve the nearby Pathfinder probe, which fell silent in 1997.
source: Wikipedia - 'The Martian' Plot Summary
I do plan to re-watch the movie closely to see if there are any further hints one way or another. If I find anything, I'll update (or remove) this response.
The Martian is based as closely as possible on real science and technology so the answer to this can be taken from NASAs own reports and explanations.
NASA wouldn’t send a 2 way radio or webcam because it actually wouldn’t be any use. The mars Rover was built to send images to earth and it does this 2 ways. First is directly to earth using its high gain antenna, this operate at 1kb/s slower then dial up and relys on the earth and mars being in the right orientation. This means it can take the mars rover up to 12 hours to be able to send a picture.
The second is to upload to a mars orbiting satellite, first you need the satellite to be in position, then once uploaded the message takes 20-40 mins to send to earth. Neither of these techniques are conducive to a real time 2 way conversation.
In fact we see in the movie that the crew of Aries iii only have direct 2 way communication with earth when they are near by. The rest of the time they are reliant on sending and receiving emails or video messages. Even when rescuing Watney nasa can listen into the communication but has no direct interaction with the vessel due to the time delay.
The scenes where Watney communicates with earth are not real time. When the first images are sent you see the team on earth sitting around waiting tense. You also see mark waiting for the lander camera to move. (By the way I never understood why he gave a no option to question 1, can you see me lol).
All this makes webcam type communication in valid, if it can take hours to send a single image how do you send a stream? And voice communication is impossible for the same, it is quicker to send a stream of text as Watney ends up doing, then setting up a voice transfer that feels like 2 people constantly leaving voice messages.
The universe of the Martian does not assume that any physics bending science has been discovered so it has to base itself in the current laws of science. Therefore no 2 way radio at all, not just on an empty supply vessel.
As an aside you seem convinced that there was a radio somewhere to salvage. If there had been either Mark would have done so, or NASA would have told him where one was or how to build one once they made contact, he didn’t and they didn’t do it can be safely assumed that there was no radio despite you seeming to want there to have been one that he didn’t use.