If you're able to leave a little earlier (1621) and possibly arrive a little later (2005) than you've set out in your post, and you're willing to tolerate a slow service between Coventry and London, then I might have something for you.
- £3.95 Advance Single with 16-25 Railcard from Coventry to London Euston, valid only on the 1621 departure.
- £16.10 Anytime Day Single with 16-25 Railcard from London King's Cross to Cambridge, valid on any service.
1) London Northwestern Railway: 1621 Coventry - 1817 London Euston
2) London Euston - London King's Cross. It's either one stop on the tube, or about a 12-minute walk (going by Google Maps timings, you might well be quicker).
3) Great Northern: 1844 London King's Cross - 1934 Cambridge OR Great Northern: 1914 London King's Cross - 2005 Cambridge.
The 1844 falls short of minimum connection times from Euston, but since your ticket from King's Cross to Cambridge would be flexible anyway, if you happened to miss the 1844 you could always catch the 1914 or any service after it.
If you're able to leave even earlier, there are some advances left for £11.90 on the 1611 Virgin Trains service to Euston, which would get you in at 1714.