I claimed a $1080 home energy credit in the Deductions $ Credits section of Turbotax (and it appears there) but it isn't in the final credit summary. Why not?

Do you have a tax liability?  The Home Energy Credits are  nonrefundable credits. This means, even if you qualify based on your purchase, if you do not have enough tax liability, you cannot claim the credit this year.  The Home Improvement Energy Efficient Credit for windows is a use it or lose it credit.  This means if you do not have enough tax liability this year, then you lose the credit as it cannot be carried forward.

Look at line 16 on your 1040, then also look at line 24. If the amount on line 16 is less than the full credit, then this is the maximum amount of the credit you use this year will be that number.  If you have other credits, that may also reduce the tax liability, this may also reduce the amount of the credit you receive.  

Then look at line 24.  If this line is $0, then you received one of more credits that brought your taxes down to $0.  If this is the case, and you had multiple nonrefundable credits, you may not get the full credit for one or more of the credits. If you look on line 16 of your form 5695, this will show any eligible carryforward, but as stated, they are ONLY for the residential energy credit, not the Energy Efficient Credit.