Should i do a ANOVA or a t-test

I have 4 groups of qPCR results and one of them is my control. For this experiment, my control group has no variance (all members of this group have just 1 as a result). I want to compare the results from the other 3 groups to the control. However, GraphPad gives an error when doing an ANOVA, because my control group has no variance (it still does the ANOVA and presents the statistical significance between groups, but it gives the error message). Can I still consider the resuls from this ANOVA trustworthy, or should I just do individual t-tests comparing the experimental groups to the control group? Thanks for the help!