Is there a test to determine whether solder is leaded or lead-free? Perhaps conductivity/resistance?
Lead-free solder has a much higher melting point than leaded. If you have a soldering iron and some leaded solder, set your iron to a temperature where it just melts the leaded stuff. Then, try heating up a component on the board at that temperature (make sure it isn't connected to a large copper pour).
If you're having trouble getting the solder to melt, there's a good chance that it's lead-free.
Use one of these 3M Lead-Check Swabs:
Keen or desperate? - measure it's specific gravity.
Compare with published or calculated data.
Take a large enough sample and weigh it = M1.
Suspend in water and weigh again = M2.
SG = M1 / (M1-M2)
Weigh = M1.
Then measure volume by water displaced when inserted into a just full container.
Water mass = M2.
SG as above.
Lead solder makes "shiny" joints when properly used.
Lead free solder makes more matte appearance joints.
Melting points vary.
Lead chemistry, various.
Based on Leon Heller's link
Various lead test kits are available.
These are usually intended for testing for lead paint but should be very effective with solder.
You can do DIY test solutions using Sodium Sulphide solution. Here is an excellent article explaining Sodium Sulphide testing for lead. This test can be used on hands etc to check for lead contamination and to show how effective cleaning proceures are.
Excellent discussion -Science Fair project starter on lead testing