Tia,
I have a few questions / troubleshooting steps for you. Normally when we see issues like this it's the raster that's not displaying, not usually the vector data.
1. Which version of ArcGIS Desktop are you using?
2. Are these feature classes or shapefiles?
3. Did you check out your data using the ArcPad Data Manager? If you did, did you check out for disconnected editing or background data? If background, was it to axf or shapefile? (Or if using 9.3.1 did you use the ArcPad toolbar?)
4. If you check out only the feature classes and not the MrSid, do they display in ArcPad?
5. If you're checking out using the ArcPad Data Manager, did you check out the MrSid as original raster format or did you manually copy the MrSid to your device outside of the checkout process?
6. Do you see the same behavior in both ArcPad on the desktop as well as your Nomad? If you haven't tested on the desktop, please do so and note the behavior.
7. Try checking out the layers one at a time (without the MrSid) and open their maps individually in ArcPad. Do you see a difference between the individual checkouts and the project with the combined layers?
8. When you say "One of my four layers is visible in the project selection window", what exactly are you referring to?
9. If you check out only the vector layers and they all appear in ArcPad, you'll probably need to take a look at that MrSid. If the same issue occurs regardless of whether the MrSid is in the map or not, you can disregard what I've written below.
I have seen issues where although the layer properties show that the raster has the same projection as the vector data, the underlying projection file for the raster is actually slightly different than that of the vector data.
Open the projection file for the MrSid in a text editor. In an additional text document, open the .prj file that's associated with the vector data. These can be found at...
C:\Program Files\ArcGIS\Desktop10.0\Coordinate Systems
Do the two files appear different (as in the information in each is in a slightly different order)? If they do, make a copy of the projection file for the MrSid. In the new copy, delete the contents via the text editor and copy and paste the contents of the prj file from the coordinate systems folder above. Swap this copied projection file for the original. Try adding the MrSid and vector data to ArcPad, do you see any difference?
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Long story short, there's probably something going on with one or more of your pieces of data. Work with them all individually to see if you can pick out one or more layers that are causing the problem. If they all work individually, then start to combine them together. See if you can use the process of elimination to determine which piece of the puzzle doesn't fit quite right.
Feel free to respond after trying some of the things above.