The cpu fan spins when plugged into 2 out of 3 connectors, in one configuration it does not. The case fan does a quick whiz then stops when plugged into any of the connectors.
In some cases a CPU fan that spins momentarily then stops is normal. Unless you're sure that the CPU fan used to spin 100% of the time before you... ahem... 'serviced' her PC?
The motherboard does some basic checks on everything plugged into it at startup. If the PC speaker is connected (properly), then anything fault (such as CPU, graphics, memory) will be indicated by a combination of beeps.
You +have+ to connect the PC speaker the correct way or it won't work, same as an LED light. They only work one way.
If you're sure that speaker is connected correctly, take the RAM (memory) out and see if the motherboard beeps at you (it should). You'll also have to be sure that you've connected the 20/24 pin and 4/8 pin power cables to the motherboard.