My first suggestion would be to bust a DMM and measure.
However, if you don't have one available then DTRs suggestion is right on. The bands are a visual representation of the resistance. Here is a nifty calculator. http://www.dannyg.com/examples/res2/resistor.htm
Otherwise, the blue disc is a capacitor while the other is a diode as mentioned.
Well, I dont know if your question was answered.. but here is what I see
the blue thing on top, looks like a MOV (surge supression device, commonly known as a varistor)
My reason to call it a MOV instead of a capacitor is the fact that I can spot a little symbol on the side and ratings that suggest to me it is a MOV.
below it, the black thing with the white stripe is a diode.
down further you have resistors (and looks like one of them was blown on half, I also spot a blown fuse next to it)
and the white boxes to the left are capacitors.
It will be pretty hard to tell what the original value of the blown resistor is, I can see a gold band (tollerance), so im assuming its different then R10.
also, the fact that it looks fried, probably means that messuring the resistance wont be accurate.
R10 is a 100 ohm, 10% tollerance resistor, indeed a 1/4W (like said, has tollerance of 10%. so 90 ohm or 110 ohm)
from a glance. this looks like part of a line filtration circuit for input mains or something. (not sure what the diode is doing there though)
Uhm, the gold color can be due to the heat, and you can see that the first 2 bands are still brown and black, as in the upper one ..... other than this, the two circuits looks identicals, and both connected to the same pin of the VDR (mov) ..... it looks as a 2 branches of the same filtering line, for me, so it's a good possibility that also the burned one is a 100 ohm 1/2W carbon resistor same as the first one.
Be aware about one thing, anyway ..... carbonized fiberglass IS CONDUCTIVE til a certain degrees ..... i mean, the board of the PCB, usually insulant, when become carbonized become conductive, so if the burned spot involve 2 or more copper strips or holes, it may alter all the circuit, and cause new blowing when powered, if left in place ..... i already had to totally remove carbonized spots from circuits, for repair them, and this means usually take away all the black burned part, also making holes in the PCB and reconstructing the connections in a second time ..... test all with a good DMM, about this, is always better than have a second "blam" when you re-power up the thing, imho
Here's something my old digital electronics professor told me once.. It's a little dirty, which makes it all that much easier to remember (starting at zero [black] and working up to 9 [White]):
Bad Boys Raped Our Young Girls But Violet Gave Willingly
You might have to highlight the above sentence to see all the letters..
Black (0) Brown (1) Red (2) Orange (3) Yellow (4) Green (5) Blue (6) Violet (7) Grey (8) White (9)
Once you know the sequence of colors/numbers, it's easy to figure the color codes out. Typically the first two bands are the first two significant figures, and the last band is the number of zeros which follow the first two sig. figs. So for a 100k ohm resistor we would have a brown line followed by a black line for (1) and (0), and then a yellow line for the (4) zeroes that follow them. this gives us a value of 100000 ohms, or 100k ohms.
on a side note. i have a new phone that runs on android and i found a free app that is perfect for laserists.. it tells you a resistors value based on the bands, it gives info on lm317 stuff and led resistor values.. it is free and called "electrodroid"
There is one thing I didn't see mentioned. Color black can never be in first place. So, a 1 ohm resistor will not be black, brown, black [zero, one, multiply by 1]
It will instead be brown, black, gold, which is 10 multiplied by Gold=0.1
This can be useful sometimes if you can't figure out which is the first and last band, first one can never be black.