I qualify for $3200 in energy tax credits but only $373 is showing as a credit, with no carryover to next year. Does this form still not work?

Only certain types of home energy credits qualify to be carried over to a later year if they cannot all be used in the current year.  

The Clean Energy Credit (solar/wind) may generate a carryover amount, but all other home energy credits have limitations applied and are not carried over if they are not able to be used.  

Your tax liability could be limiting your energy credit to a number less than you expected.  You can take a look at your Form 1040 line 18 and line 20 to see if that is the case.  Line 18 will show your tax liability and line 20 will include all the credits shown on Form 1040 Schedule 3, including home energy credits.  Line 18 must be greater than lines 19 and 20 combined to take full advantage of the home energy credit.