Advance Inverness - Glasgow Queen Street leaving at 1247 and arriving at 1615: £10.30 (can travel earlier for the same fare if you want to)
Walk to Glasgow Central
Advance Glasgow Central - Birmingham New Street leaving at 1740 and arriving at 2148: £21.00
Total £31.30
Alternatively there is a direct Advance available via Edinburgh, leaving Inverness at 1451 and arriving Birmingham at 2255 for £37.50. I haven't tried going via Manchester or Crewe but this seems pretty cheap to me. I suggest booking soon as most of the tickets are pretty expensive.