In order to apply a t-test between two samples (which is, at the end of it, what limma is doing - albeit in a fancy way) we need to know three things about the two samples.

- The mean
- The sample size
- The variance (or more specifically the standard deviation)

In your case you have an estimate of the mean (the measurement of expression for a given gene on your one replicate per sample) and the sample size (1), but you have no way of calculating the variance (if we assume the two populations your samples are taken from are independent - a reasonable assumption, given the hypothesis we are testing).

Even if your one measurement gave us a good estimate of the mean (and this is by no means certain - there are many, many reasons why your sample could be an outlier), without the variance we simply have no route to calculate the t-statistic for the tests.

For this fairly simple technical reason, it is impossible to apply limma (or indeed any valid statistical test) in a situation where you have no replicates in at least one of your sample groups. This is just one of the many reasons why replicates are _absolutely required_ when doing microarray (and indeed, RNA-Seq) experiments.

See also: Microarray data WITHOUT replicates. Any hope to get something out of it? for a more general view. This is sort of a universal answer. Btw, I do not recommend to close this question because it has a slightly different focus.

Just curious, how many replicates do you require to get good results from LIMMA. In other words does LIMMA have any recommendation on the number of replicates?

This kind of analysis is called power analysis. If you search for "power analysis microarray data" you will find several tools, e.g. the BioC package SSPA.