You should not count the number of pulses, but the number of transition from 0 to VCC volts or VCC to 0 volts (called rising resp. falling edge).
If you don't want to solder, you can also use a light dependent resistor (LDR) very close by the LED to measure the difference in brightness. See also chrisl's remark below.
The counting you can do manually (in a loop, check as often as possible or needed), or by setting up a timer to check for either rising or falling edges.
I will give the pseudo code so you can figure out the actual code:
unsigned long int _counter;
// Set Serial
// Set LDR
_ldrPin = readAnalog(X);
if (!_ldrPin && readAnalog(X) == HIGH)
// Rising edge, increase counter
_ldrPin = true;
else if (ldrPin && readAnalog(X) == LOW)
// Falling edge, reset status
_ldrPin = false;