To better check if the leak is coming from the inlet try checking the air at higher and lower carrier flows(low oven temperature though to prevent damage to the column from the air). If the air goes up with higher flows it could be somewhere before the injection port, not just at the injection port.
What manufacturer is the GC?
If Agilent, the gas lines going into the injector top can get very tiny cracks where they pass through the shield attached to the top and can be difficult to diagnose until they become larger.
Another test you can perform is capping off the column by pushing the injector end into a septa and see if the air becomes less and the source pressure drops, if it doesn't then you could have a broken column.
If the column is new, and has just recently been installed, check the nut where the column enters the MS as those tend to shrink in the first few days/oven cycles when new. This can often appear as a high air background at low oven temperatures that goes away as you increase the oven temperature during an analysis cycle.
Good luck, I hope it is a simple fix
