I'm thinking a PIR sensor (available from many places -
ebay $9.99 link
Adafruit $10 + P&P link )
Together with a microprocessor with a serial interface e.g. ATTiny2313v $1.48 from mouser link. The ATTiny will run with no additional components, using an internal oscillator. You may need a bit more memory (RAM/Flash) than this but even an ATMega168 is not too expensive.
Use a SD card to store the data in (fast and non-volatile) - can be interfaced directly to ATTIny via SPI (need a SD card holder). No need to use FAT as the data can be read out by the controller into the serial interface.
Use the serial interface to plug your laptop into (bring a USB-TTL serial convertor).
So with enclosure and assorted connectors etc you will probably come in at about $20.
The PIR operates at 3.3v (you can bypass the 3.3v regulator to do this) and the ATTiny will work quite happily at that voltage.
Battery consumption is the only other issue here - PIR consumption is the one to worry about here - the microcontroller can run in full sleep mode (micro amps) almost all the time, waking the microcontroller up via an interrupt when the PIR detects something.
The PIR is rated at 4.7mA when run from 12v. You can get rechargable AA cells with around 2000 mAH, or LiPoly cells - so these would last just over two weeks.
So all in all yes it is possible - but it may cost a few $ more than your budget.
You can attenuate by using thin sheets of polyethylene. Polyethylene is the same material that the PIR lens is made of. It will pass, but attenuate the wavelengths you are interested in. Find something around .015" and begin stacking until you hit your desired range.
Here is a source: http://www.mcmaster.com/#polyethylene-plastic-sheets/=hc4uvj
Best Answer
People often use imprecise terms to describe InfraRed and it is further complicated in that with respect to Infrared "that word infrared ... I don't think it means what you think it means" in a lot of cases.
PIR - AKA Passive infrared sensors are pryoelectric devices that are optimized to detect Mammalian body temperatures (around 300 K), these warm bodies emit light at around the 10µm to 14µm wavelength range. Some people call this the "mid Infrared" but the trend is towards using the term "Thermal InfraRed" or TIR.
The IR LED you are using emits probably around 900 nm -> 750 nm - so close to 1µm in wavelength. Some people call this "Near IR" but those people also tend to call 2 - 4 um wavelngth range the "Mid Infrared also". Confusing? yep. It comes from a different historical use. One from the military one from chemistry/astronomy.
So you are at least a factor of 10X away in wavelength terms. And a LED emits light in a very, very narrow band of energies (it is an electronic effect after all)
Also PIR's are "designed" to detect rather largish bodies, which means a fair amount of energy or photon flux.
A black body emitter will increase energy in all wavelengths with increasing temperature. So an emitter at 27 C (300 K) will emit less light at 10µm than a emitter that is at 100 C (373 K) in the same band of energies. So if you want to have an emitter that will trigger the PIR, make a temperature controlled emitter, run it at 100 C to be safe, and it will emit a lot more light in the 10 - 14µm band than a body temperature device.
On second thought make it 70 C just to be safe. 100 C is a little too hot. Read up about blackbody emitters for fun.