I have been to India before, but have since renewed my passport so have no record of previous visa details. What does one do about completing this question online?
If you cannot prove that you have been to India with the respective passport & visa or a copy of it, your only choices are to either answer accordingly or simply state that you have never been there.
Since your passport number most likely changed between passports, it's very difficult for the Indian authorities to track back if it is you who has been to India before or someone else with the same name. So from their point of view, you have never been there anyhow.
What you have to decide is how much you want to prove that you have been to India before in order to improve your chances to get a visa again. If you are from a country that is likely to get a visa anyhow (UK as opposed to Pakistan), I would not worry too much and simply say it's your first time. Saying that you did not keep your old passport (which you really should keep), might be even something that the visa officer dislikes.
On the other hand, if you are from a county such as Pakistan, I would do whatever you can to prove that you have been there. Be it with old receipts, travel tickets etc, or, if possible, find your old passport. Go to the Indian embassy in your country and talk to them about it.