Use this at your own risk, you could smoke your ATmega chip and/or your parallel port.
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OK, that’s out of the way: I built a vaguely similar one (it used the 74244 and the parallel port).
it omitted R1 - R6, R13 - R18, C2 - C4.
for R7 - R12, R21, R22, R23, I would use the next higher value I had available.
for Q1, substitute any NPN (watch for reversed cases).
R19 and R20 appear to be weak pullups? I would use anything above 50k, I would probably try anything over 5k if that was all I had.
C1 looks like your basic “digital transient filter” cap, omit if you feel lucky, use anything you have if it is flakey without it.
Don’t forget that resistors can be combined: two 1k resistors in series (one after the other) makes a 2k resistor. two 1k resistors in parallel makes a 500ohm resistor. Google for “parallel resistor calculator” (“series resistor calculator” is just addition).
desolder resistors off of any old junk lying around. google “resistor color codes” for information, or even a calculator that will tell you which colors to look for.