Some generalities to start with. There is no firm answer to the question “Which was India’s first long-distance train?” The present Railway administration seems to have decided that the Punjab Mail from Mumbai CSTM to Ferozepur is the oldest, having started its run from Bombay VT to Lahore in 1912.
While the dates of opening of different sections of track are well documented by the railways (with a full directory up to 1964), the date of introduction of trains is not so clear unless one looks at the old timetables, which are generally not accessible to the public. Anyway, some of the oldest trains would include:
Bombay-Poona Mail: probably soon after the line was opened in 1863. Was known to be running in 1869. However, the name vanished around 1971 when it became the Sahyadri Express to Kolhapur with the same timings between Bombay and Poona (which were yet to become Mumbai and Pune)
Madras-Bangalore Mail: probably soon after the line between these cities was completed in 1864. At that time it would have run between Royapuram (then the only terminus in Madras) and Bangalore Cantt (likewise for Bangalore). It would have started running from Madras Central after 1873 and from Bangalore City after 1882. It still runs on this route, although the stations are now Chennai Central and KRS Bengaluru.
Then there would be the Kalka Mail, which started as the Delhi-Calcutta Mail in 1866 soon after the last link of the Yamuna bridge was opened. At that time it would have run by the Sahibganj loop which was the only connection between Calcutta and the North then. It would have started running via the “main line” between Asansol and Kiul after 1871 and via the Grand Chord after 1906. And it would have been extended to Kalka after 1891. So this is also one of the oldest fast trains of India, despite the numerous changes of route. It is still running between Howrah and Kalka by the Grand Chord.
The Delhi-Karnal-Ambala-Kalka line was opened in 1891. Possibly the Kalka Mail ran via Delhi-Meerut-Saharanpur-Ambala at one time, as this longer route had more commercial and military significance.
I am not actually sure when it started running via the Grand Chord, as that covered relatively unpopulated areas compared to the main line via Patna. This can only be answered definitely by seeing timetables from 1906 onwards. In the 1930 timetable of the North Western Railway the abstract timetables show it running via Patna. But in the 1935 Bradshaw it is running via Gomoh on the Grand Chord, where Netaji is supposed to have boarded it in 1941.
In the same way many of the older Mail trains would have started running soon after the routes were completed. Some which must have started running in the 19th century include the Madras/Mangalore, Madras/Bombay, Bombay/Calcutta via Allahabad. By 1910 the Madras/Howrah and Bombay/Howrah via Nagpur would have started.
Some like the Punjab Mail from Bombay (1912), Frontier Mail (1928), and Deccan Queen (1930) are well documented, although the second one became the Golden Temple Mail in 1996.
The Delhi-Madras route never had a mail train. The last link between Balharshah and Kazipet was completed in the late 1920s in what was then the Nizam’s State Railway. This Grand Trunk Express ran for the first few months from Mangalore to Peshawar, then for a few months from Mettupalaiyam to Lahore and then settled to its long-term route from Madras Central to Delhi.
By the 1950s most trains from the West and South started terminating at New Delhi which had been a tiny station until it was expanded to be a station fit for a capital. Ultimately the GT was extended to Delhi Sarai Rohilla a few years ago. A number of long distance trains suffered the same fate due to the lack of stabling lines near New Delhi and Delhi Jn.
And Sarai Rohilla is one of the most inaccessible rail terminuses in India’s major cities, though it gets good competition from Kolkata Terminus and (to a lesser extent) from LTT and Bandra Terminus in Mumbai. However, unlike in Mumbai and Kolkata many of these trains also have stops at New Delhi or Delhi Jn, so it does not affect reserved passengers that much. Those going towards Rajasthan and Gujarat may prefer the 2-minute halt at Delhi Cantt to the inaccessible starting point.
Most of the trains mentioned above have separate articles on Wikipedia and other sites like irfca.org . Some sources are reliable, others are not. Anyone who says that the Punjab Mail of 1912 is the oldest train is clearly wrong.
To come back to the original question, the oldest long-distance train running on (almost) the same route throughout the years is almost certainly the Chennai/Bengaluru Mail, though the management of the CR and the NR would not like to hear that.
A footnote: some old timetables of India (including pre-1947 India) can be seen here:
http://www.irfca.org/gallery/Heritage/timetables/
It is not very systematic as bits and pieces have been added by a large number of people. If you expect to see the full all-India timetables for a particular year you will be disappointed. Some attempt has been made to give the full timetables for a particular company or zone, for instance the NWR from a 1943 Bradshaw:
http://www.irfca.org/gallery/Heritage/timetables/nwrtt/1943/
and the Jodhpur railway, 2 pages from the same Bradshaw:
http://www.irfca.org/gallery/Heritage/timetables/Jodhpur1-1943.jpg.html
http://www.irfca.org/gallery/Heritage/timetables/Jodhpur2-1943.jpg.html
There are also a few pages from the NWR of 1930 and Assam Bengal Railway of 1929. But basically you have to find your own way in this site.
Another section of the irfca site which may interest you is:
http://www.irfca.org/~shankie/famoustrains/famtraindqn.htm
although this was prepared over a decade ago and all the information may not be accurate.
Some railfans have acquired soft and hard copies of old timetables by various means over the years. If you expect them to put up the scans of the full timetables of the past, it will not happen because either the books are bound in such a way that scanning is difficult, or the pages are too yellow and/or fragile, or they are the result of multiple photocopies and are not very legible (the ones mentioned above are examples of this).
Anyway, I have been requested to summarize the timings of the Kalka Mail and Frontier Mail over the years. Probably the best you can expect is a summary of timings at some important stations retyped here.
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