I want to find correlations between change in log2(gene expression) and change in log2(VO2max) from time A1 -> B1, adjusted for group and including the fact that the samples are paired. I get this error:

"Error in glmFit.default(y, design = design, dispersion = dispersion, offset = offset,  : 
 Design matrix not of full rank.  The following coefficients not estimable:
 ID79"

Is this due to some linear dependencies? How get I get the results I want?

VO2max <- as.numeric(pData.myoglu[ 1:52, 6]) # (Random numbers as I can't post the original here)

Time <- factor(pData.myoglu[ 1:52, 4], levels=c("A1", "B1"))

Status <- factor(pData.myoglu[ 1:52, 2], levels=c("control", "IGT"))

ID <- factor(pData.myoglu[ 1:52, 1])

design <- model.matrix(~ 0 + log2(VO2max) + Status + Time + ID)

Here is the design (not enough space to paste):

http://imgur.com/4H9TUS2

Yes, it is because of linear dependencies. There's no way to tell what exactly the problem is, because you don't show what the experimental design actually is. I'd suspect that it is something to do with the three factors, i.e., time or status or ID, and how they correspond to each other. As a hypothetical example, if all samples at a certain time also had the same status, then there'd be no point putting both in the design matrix.

You have what is called a multi-level design in the limma and edgeR User Guides. You haven't told us what 'ID" means, but let's assume that ID corresponds to patient, for the sake of argument. The study has one within-patient factor (Time) and one between-patient factor (Status). You can't just add everything together in a linear model because ID is confounded with Status. Have a read of the User Guides.

All my comments about multi-level designs remain true whether or not the continuous variable log2(VO2max) is included in the model. But let me add that it is unusual for a continuous variable to be at all sensible in the paired design. You are basically trying to fit too many things at once to the same data. I suspect that you would to do better to remove either or VO2max or ID from the model.

Whenever you add a factor or covariate to the linear model, it means that all other coefficients in the model are adjusted for that factor. When you add ID to the model, it means that all the other coefficients can only be estimated from the within-patient comparisons. Since the same patient always has the same status, it becomes impossible to test any difference between IGT vs controls.