If not, was there ever a record of this available? What happened to these records? If available, where can I find them?
I think the short answer is that you are probably out of luck. In the vast majority of cases, the individual data does not survive and is therefore not available.
As noted on the Families In British India Society (FIBIS) wiki:
There are very few census records available to help you trace your ancestors that lived in India. Censuses were taken, mostly on a regional basis with the earliest comprehensive census taken in 1870/71, but no "as enumerated" data survives. Statistical reports of censuses are available and have been digitised by a consortium of Australian Universities.
- my emphasis
The FIBIS wiki notes the few known exceptions, where some of the enumerated data for individuals survives:
1851 Bombay Presidency Mofussil Districts - European Residents only. The data from this census is accessible through FIBIS Search.
1840 Serampore (just north of Calcutta) - this was then Danish Territory and a complete census was taken of the population, including natives. European & Indo-European names are available through the FIBIS database 1840 Serampore Census transcribed by Sylvia Murphy. The records, in Danish, have been microfilmed by the LDS (Mormons), with this Library Catalogue entry.
1834 Tranquebar - Madras Presidency - again this was Danish Territory at the time and the Danish 'as enumerated' data has been preserved and has been filmed by the LDS [Church of Jesus Christ and Latter Day Saints], with this Library Catalogue entry.
1790 and 1834 Tranquebar census are included at the end of transcriptions of church registers at Tranquebar Registers. See Tranquebar.