ok, do this:
make a crossover cable using two DB9F connectors using simple three wire connection (2-3, 3-2, 5-5).
use it to connect two com ports (either two PCs or two com ports on a same PC).
open one Hyperterminal (or whatever other 'therminal' you have) for
each port and set them up for same baud rate and click on connect icon (both terminals!). since we use simple cable there is no hardware handshaking (choose 'none').
If you type something in one terminal, same text will show up on another.
if you try to type on other, that text will show up on first one - just like in ICQ for example.
Now if you disconnect one end of the cable and plug it to some other device (anything with RS232 port), you can see what that device is sending and if you want to 'talk' to it, just type message or command it can understand.
now some devices will require straight cable. this is normally required for
'dumb' devices that normally cannot initiate connection (google for more info on DTE and DCE).
we use this approach all the time to communicate with all kind of devices (printers, vision systems, barcode scanners, industrial servos, HMIs and whatever else comes our way).
74LS04 is not too slow to turn LEDs on and off - it is way too fast for your eyes.
that's why the LEDs appear to 'dance' - they are turned on and off many times per second.
you can make some shift registers for example to capture streams but it's not worth the trouble. most messages are 20-200 characters long and each character is one byte (8bit). since you are trying to work with discrete components, that means some 20-400 chips, 160-1600LEDs etc. even at $0.05 per LED and $0.50 per chip you are looking at some spending, lot's of wiring and troubleshooting etc.
by the time you are done looking for suitable breadboards in your catalog of choice, you could have tried out hyperterminal and be playing with communication.
if you have any programming software (VB, Delphi, Pascal, QBasic, anything...) you can write your own terminal. This would have big advantage that you could use it to not just send/receive but also generate codes and act in a certain way depending on response from device. yes this can be done manually but it can take veeeeery long time and it's so much faster and more comfortable to make computer do bulk of work for you, have option to save and load bunch of data so you can really study it.
without saving data, i mean by looking at LEDs you would have to record all bits manually. you don't want to use paper book for this do you? how do you compare thirty strings to look for paterns (even if your handwriting is not too bad)?