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If you can convince the customs officials that there is no commercial purpose, you will be able to bring them just fine.
For your broken laptop, note that you will probably have problems taking it over customs because as far as I know, your laptop must be in working condition. See more from here.
In Chennai, you can explain the officials (Tamil/English) that you are using one for your work, and the other one is already a used one. A couple of tabs is usually OK. You have up to 45,000 INR allowance (link) for short stays.