I recently bought a Techsun PL-660 radio and it picks up virtually nothing on SW. I fear I may have a dud.
The primary factory controlling SW reception is your antenna. Find the antenna antenna input (marked 'FM and SW Antenna') and connect it to a wire of at least 50 feet in length (longer is better); route the wire outside of your house, if possible. Ideally, it should be mounted high up in the air, on poles, to get it away from the earth. The antenna wire can be bare or insulated, but try to keep it away from metallic objects, transformers, electric wires, etc. The wire should be mounted using insulators, so it can't lose signal to ground. If it goes outside, use an insulated wire where it comes into contact with walls, windows, etc.
If you want to pull in more signals, try a high-performance receiving antenna. You could consider a magnetic loop antenna like the Wellbrook Loop, or the W6LVP Loop. They cost more, but are outstanding antennas. I use a Wellbrook Loop with my KiwiSdr; it covers 10kHz to 30MHz.
We definitely need more information to answer appropriately, but I'm willing to answer as best I can with the information given. The receiver you have chosen is referred to as an Ultralight and is generally regarded as a decent performer. I am not aware of any significant issues although there are always possibilities of "duds" in any receiver line.
You say "virtually nothing"; So that means you receive something. Good. What was it? When were you listening? How was the sound quality/signal quality? What other times have you tried and what were you expecting?
There are currently at least 50 to 75 countries left broadcasting on shortwave these days. There may have been more in the past, but there still are quite a few. It's true that many of the major European broadcasts to North America in our evening hours have ceased, but shortwave is still alive and well in much of the developing world. One simply has to look at the last few issues of Glenn Hauser's excellent "DX Listening Digest" to see that there is quite a bit on the air to hear, especially in part of the world such as New England.
A casual tune across the 49 m band in your local afternoon or early evening should produce at least a dozen countries spread across North America, Europe, Africa, and South America broadcasting in various languages.If this is not happening, I would first suspect a local noise source is blocking the signals, especially if you are indoors. As an amateur radio operator you are no doubt familiar with how much RFI has increased in a typical household in the last 20 or 30 years. So, with that in mind, look to options such as listening outdoors to see if the problem goes away, connecting to an outdoor antenna or even a random piece of wire put out the window, etc. You can also use the Tecsun on batteries that mouse grid to try to hunt down the source of the noise.
Please let us know what you find.