"What are they" Revised: They are decoupling capacitors. I found a great page that lists every part in the 360. Motherboard, Bottom CPUPassiveCapacitorQUANTITY 256 Ceramic Multilayer - X5R/X7RBrown04022 http://www.electronicproducts.com/whatsinside/viewteardown.asp?filename=Xbox_360_web.html So I guess now the question is how do I measure or find out the capacitance.
Judging from all of my arcade boards, I'm pretty sure those are just jumpers. They could be unmarked resistors, but those are rare to find in such a clean configuration. You could always pop off one of the good ones and test it.
Wait, why would they make big chunky things like that if simple PCB trace would do? Surely it's capacitors? A multimeter will tell all, regardless.
So, judging by the picture and how the solder contacts looks, it looks like you're missing more than one of those things. At least 3 and one of them is looking loose next to the arrow. I always thought those were resistors. Anyway, I have had experience changing them out on motherboards. I just replaced them with similar looking ones in both size and color as there are different types. As far as measuring capacitance, I have no idea as I am not that skilled in PCBs.
If you can, talk to a local Uni/High school. Back in my college (16-18, so equivalent to a high school) we had an LCR databridge, which would read capacitances to a pretty precise value (around 5-10% i seem to remember). Also, here at university in the Electrical and Electronic engineering dept (Mine!) we have numerous sensitive Capacitance measuring apparatus. If you can somehow blag a go on one, you should be able to tell the capacitance straight away.
There's at least 4 broken, possibly a fifth in the lower right area of the breakages. Obviously there aren't any markings so just replacing with something that looks "similar" isn't a good idea
Yes they are surface mount capacitors. The letter C on the PCB stands for capacitor ;-) Measure them out of circuit, i.e. desolder them. You'll need a good eye with a soldering iron, or use an airflow gun (SMT gear, basically). Most decent multimeters nowadays have capacitance meters built-in. Hell, I bought one for around $15 that had one! That or an LCR bridge, if you know how to use one. They're likely to be between 10pF and 0.47uF. Oh, or you could check the code and use a SMT capacitor catalogue to look it up ;-) Usually it'll be a 3-digit code (two base numbers and a multiplier in pF, e.g. 470 = 47pF, 472 = 4.7nF), or a 2-digit code, which is a letter for the value, followed by a number for the multiplier. I can't think of the values offhand, sorry. Why do you want to know? It is very unlikely that they will be faulty, if you're thinking about replacing them.