If you wish to practice as a CS then all those conditions need to be satisfied, before applying for membership to ICSI. If your intention is only to pass the CS examination, you can go ahead and pursue the course, subject to conditions laid out by ICAI, (permission from the Institute is necessary if you are undergoing article-ship training).
Kindly also note that the syllabus and fee structure of CS course has changed w.e.f 1st February 2013.
ICSI allows exemption in some subjects on reciprocal basis to students pursuing CMA (ICWAI) course only and not to CA students. On Computer training, that should not be an issue, where in you need to pay some adequate fees and take up online test at some ICSI designated centers.
For further clarification kindly visit www.icsi.edu