I got some MIDI from the web and I can't find anything wrong with the data but the tracks won't play. Bass for example, I add it to my own existing track and it won't play. The track plays all the notes I put in myself but not the new ones from the web, it just doesn't seem to know they're there. 
If I add a new bass track and new bass instrument, then it plays but I can't get it to play on the existing bass track. The notes are all within range, MIDI data is being sent and there's nothing in the data (such as volume off).
 
Thanks - rev

is your midi tracks sent to a softsynth?

Make sure the notes are in the proper range for the synth.
 
Also MIDI files can include data that will shut down the sfz engine used by Studio Instruments, Session Drummer, Rapture, Rapture Session, Rapture Pro, Dimension Pro and Cakewalk Sound Center. Usually this data is at the very beginning of the clip. Here is a post on how to handle this issue.

TTS-1 should always play a downloaded file. But others like SI Bass always need the part transposed +12. 
As scook has said. Some free downloads were not pure GM and need editing to make them work. 
If the data is there it will work. I almost always open the file in the event list and delete a lot of the controllers. You can also do this in PRV with eraser tool. Look in the control pane to see the list of what is there.  
Some controllers will not play nicely with a lot of the better VST's. 
 

• Data is being sent to a bass soft synth
• Data contains nothing but notes, no controllers
• Data is within range of the instrument
• If I copy any number of notes to the track that's working, they simply get ignored
• If I enter all the notes myself, they work.

 
But that was what I was trying to avoid. I've had to do it because nothing else worked.
 
rev

Midi channel? 
You said you copied some notes? 
Look in the event list for the track. What does that show? 

^^^ Event list should be your first stop in the investigation.
 
The notes could have a zero velocity value, or be assigned to a different MIDI channel. Make sure your synth's MIDI channel assignment is set to "omni".