This sounds like a rather easy and fun project.
Take any Arduino and connect the current measurement gate hardware. This will take some tinkering, but probable is pretty straight forward. If needed, you can make your own measure points too.
For the upload, send the data via USB (as a Serial device) to PC. If this is a dedicated PC, consider using Linux, but Windows is just as fine. You just need to write a program that reads from the correct virtual com port and does with the data whatever necessary. I would go with a simple protocol where per measurement a text string is sent, something like:
lane;lap;time (eg: 1;25;10.354)
For the fun part - if you don't already have it - connect a few 7 segment LED displays to show laps and or lap times and 1 or 5 buttons to reset the lap counter (either just one global or one for each lane one) That way, the thing can be used without PC.
All in all, you will need is an Arduiono Duemilanove or Uno or compatible with an USB on-board, a hand full of cheap components (some 74HC595 or serial 7 segment led drivers if you add a display) and some time to tinker. I would budget some ?50 for the hardware including the Arduino.
Korman