I'm afraid that you will not be able to integrate the plasmid employing the URA3 locus in the strain (By4742) if it is carrying a full deletion of the URA ORF. Without the endogenous URA locus present in the genome, there is no possibility for crossing-over event to occur with the endonuclease digested vector you are transforming with (cut site within the URA3 locus). (Further, if you wanted to use the vector undigested as a CEN plasmid you need to have a mechanism on the plasmid like a CEN or 2 micron on the plasmid for the vector to be retained in the yeast strain).
However, if the vector you are trying to integrate carries a yeast gene, then you could integrate using the locus of the gene itself. Be careful to select only a single restriction site within the yeast ORF and have the recombination even produce a full length ORF with the mutation/tag occuring downstream from the endonuclease site.
I hope this answers your question...there are troubleshooting approaches to the LiAc/PEG technique, but from your post, it sounds like you might need to redesign your experimental approach...