Many circuits may not work at all with weak batteries (let alone dead ones).
REALLY SPEND TIME with ONE PROJECT at a time:
Get a basic MULTI-METER (also called a "VOM" for "Volt/Ohm Meter", or "DVM" for "Digital VoltMeter"), and learn how to use it. Cheap ones ($5-15) -- either digital or analog -- are available from the electrical supplies sections of Wal-Mart, Harbor Freight, and various hardware, automotive and electronics stores.
If you can afford it, buy one of each type ("analog" with a moving needle -- and "digital" with a digital display) -- they each have advantages and disadvantages. Combined, they're really handy.
Just keep in mind that most components have a certain amount of "slop" in them:
Their component's official or marked ratings may be very precise,
but the component, itself, will probably only be approximately that value.
The range of acceptable or intentional variation of a component, or a circuit, is called its tolerance. Many resistors, for instance, have a "tolerance" of plus-or-minus (+/-) 20%. (A resistor marked as "100 ohms" may actually be anywhere in the range between 80 and 120 ohms.)
REPLACEMENT PARTS are available (usually cheaply) from: