(Note: I don't have relevant expertise, so a lot of this is speculation.)
There are a couple problems I see on a planet without life. The first problem to consider is accessing carbon. Most carbon would be in the form of carbonates, which would have to be mined, and the carbon would have to be extracted. If the planet is cold like Mars, there might be frozen carbon dioxide. There would be carbon dioxide in the atmosphere and oceans as well, but extracting useful quantities would be difficult would require processing huge amounts of air/water.
Carbon dioxide and carbonates are quite stable, or they would react with something else. So they will require either energy or some reactive chemical to convert into a useful form. And without biotechnology, catalysts are limited, so at some stage they'll need large amounts of energy to access some necessary material.
That leads to the second issue, energy. Without hydrocarbons available, the main energy sources will be solar or wind/water/nuclear/geothermal powered turbines. The major problem I see here is a lack of plastics for insulating wires and electronics. Ceramics will be able to fill the role of plastics in some situations, but they will also be partially limited by the lack of organic precursors. Since electricity is so useful, I think they will find a way to make it work, either by finding inorganic substitutes or by devoting a large portion of their energy to producing the plastics needed for upkeep on their energy generation. However, this energy generation is likely to be inefficient, at least until they can take advantage of economies of scale. This also makes mining, smelting etc. more difficult.
The last problem is organic synthesis. I don't think much is impossible. Simple reactive molecules can be produced by applying energy or heat to nonreactive materials. These can then be used to synthesize more complex molecules. Humans also have large amounts of microbes living on and in their bodies. The fact that there are a small number of humans means they can eventually redevelop biotechnology - although most microbes likely won't survive outside human habitats. The problem with organic synthesis is that it will be extremely expensive due to the lack of available carbon. It will also take a lot of effort to figure out how to make complex organic molecules. Thing like biologically-derived medicines and catalysts will be the most difficult.
So to sum up:
- It will be possible to make most substances, or acceptable substitutes, but specific complex organic molecules (i.e. medicines) will take years or decades to develop and can only be made in tiny quantities.
- Any organic (carbon-containing) materials will be require a lot of resources. Large plastic objects will be prohibitively expensive.
- It may be difficult to transmit electricity.
This suggests a few general principles to me:
- The technology is designed to take direct advantage of natural resources. Technologies like geothermal forges, wind/waterwheel-powered factories, sailboats, use of natural caves for shelter, etc. will allow the inhabitants to avoid wasting electricity.
- The technology is designed to produce as little waste as possible. A lot of effort is put into designing technologies efficiently to avoid waste - think things like honeycomb designs for metal struts to avoid using unnecessary material. The effort of designing something correctly is always less than the cost of using an inefficient design.
- Organics are mostly only used for electronics, medicine, basic needs like growing food and clothing for the humans. Most large objects are made of metal, glass, rock, cement, or ceramic.
- Reducing, reusing, and recycling is extremely important.
The limits on plastic are a big difference. Almost everything is painted to prevent wear and tear - it will need to be armored or glazed or galvanized or covered in cement or clay instead. Rubber tires are crucial for transportation - expect more boat, rails, and walking robots. There's no wood - furniture will likely be made of concrete, and bedding might be made of sand, or flexible wire mesh. Clothing and protective gear would be difficult to make.
The human population will likely remain small, due to the large amount of carbon required to sustain human life.