Here we go.......but take a look at the caps along side the IC....I think they look a little suspect?? Only noticed them in the pictures when posting this...
1) The cap sleeves look all melted somehow.
2) I found the datasheet for FS9721_LP3. I'm reading it now to try and understand how it works.
3) While I do that, I have 3 more things for you to measure. All are resistance readings.
i) Marked in yellow are PTCs. I believe they should all be around 1K ohm from reading the datasheet. You may have to desolder these 3 to get a accurate reading?
ii) R26 (in blue) should be a 10M ohm resistor. Measure this in circuit and verify that it 10M.
iii) R31 (in red) is a 10K SMD resistor. Measure this in circuit and verify that is 10K.
4) BTW, rumor has it that the Fluke 15B and 17B use the same FS9721-LP3 processor. Certainly the specs for the Fluke 15B and 17B match up with the FS9721-LP3 datasheet.
5) A really good SMD soldering video is here
http://www.youtube.com/watch?v=3NN7UGWYmBY6) Of course Dave Jones also has a 3 part soldering video and demonstrates various techniques for SMD.