Wiring a new thermostat without a C wire, extra wires from furnace
You said your old thermostats C-Wire did not work so you wired a new one.
You said your meter only measures 50V or higher (I never saw a tool like that before) - so how do you know the c wire was not working? 

Your old thermostat was not working ? 

Your old thermostat picture shows something like this:

C or G?? , [Y?orX? - most likely Y], W , [RH RC] 

It would have been a better photo if the letter codes were visible; these codes are standardized and they do have meaning as to what circuit they operate.

Common (24VAC) - should be a black wire - blue is for other things, G is for Ground green wire ,  if Y Cooling On Signal [Most likely Y for Yellow] ,  W Heating on Signal - white wire , [ Rh 24VAC Heating , Rc 24VAC Cooling  - red wires ].

The additional wires that you show removed - I am thinking out loud here - they go to your outside Air conditioner Condenser? They turn it on. You can check the wiring diagram for the condenser to find out for sure - and ohm the leads ..by opening the condenser panel - disconnect the red and white wire that goes into the unit - tie them together - then go back inside and measure continuity - if continuity - then you know which wires go to the AC unit - put the wires in the condenser back to the way they were before and connect the wires inside to the proper terminals. Red probably ties in to your Yellow Wire that is wrapped, and the white wire to the common - (Black tape the white wire so you know it is really black). 

Now if they do not go there - then they must turn something else on - that will need to be verified where they really go to by continuity testing .. but I think the AC Condenser is where they go. 

I can't see your Air Handler control board terminal labeling very well - so under the white wire - the label is ? and next to it is that a Y ? for Yellow like if AC is on don't allow heater to run ?

Your yellow line is not hooked up so it goes somewhere - perhaps to that Y terminal on the AH control board and something like the red wire ?

The answer here has a layout of what wire is what and the proper color scheme - although there are some missing exceptions like X which could be a heat circuit if I am not mistaken ..

Oh and by the way if all else fails - and you have not done so already - Please check your circuit breakers and check for any fuses that you might have in the system - just in case (sometimes that old adage of making sure we really have power gets skipped - especially when we have pulled things apart and perhaps mislabeled something or did not take note - figuring that out makes people forget that simple stuff - even the pros - we are all human. I remember having a 20 year old washer and dryer set - I replaced the timer in the washer and my dryer went out a month later - I had no heat but it spun - with no time to spend checking anything I quickly ordered a timer as I assumed what my problem was. Upon pulling the dryer out and getting behind the unit - I did that yes let me check the power before I go digging.  One leg of my circuit breaker in the service panel was blown. I had that Homer Simpson moment Doh!