Look at the Mass Air Flow Filter (MAF) - when this part starts to fail, it often exhibits the symptoms you describe. A quick test is to disconnect the sensor and let the car run using a default map - if it runs better, you know you have a failing MAF sensor.
Porsche Boxster Mass Air Flow Sensor (MAF) Replacement and Troubleshooting - 986 / 987 (1997-08) - Pelican Parts Technical Article