If I recall correctly, the serial port (3.5" stereo jack) on the cp505 is output only. And it runs 1200 baud, 8 bit data, no parity, and 1 stop bit as Fred already mentioned. Check that the pinout of your stereo to db9 adapter is correct (see http://www.reliableracing.com/...s/tag/TAG-Cables.pdf).
I am also not sure if data is always output on the serial port or not. I found an old manual, but my German is rusty (https://www.msc-aldingen.de/im...Heuer%20CP%20505.pdf)
If your cabling is correct and the 505 is setup to output over serial, you should see ascii data output when manually triggering start and finish inputs. I am also not sure what the framing of the data is. It could be that a control character is causing putty to erase any data before you can see it. I recommend throwing together a quick java or python program that just logs raw bytes from your serial port so that you can reverse engineer the data formatting.
In the end, you are going to have to capture any timing data as it streams out of the serial port and then convert it to a useful format for your program.