You mentioned it is one week old blood sample which is kept in refrigerated.
Generally, Ficoll histopaque will give you best isolation of PBMC when you use fresh blood sample. If you use refrigerated samples, the RBC contamination in the PBMC will effect your live/ dead assay..
If you want to isolate lymphocytes in refrigerated samples , you can try lysing RBC by using RBC lysing buffer, which is more appropriate compared to ficoll histopaque.
Samples stored in refrigerator for one week will give more dead cell.
You can check the live and dead cells by using typhoon blue assay
I agree that you will get a lot of red cell contamination after a week of blood in a fridge. Longest i have done is 24 hours.
I would recommend using the STemcell companies protocols for ficol seperation, they have some tubes especially designed to help you if you are inexperienced.
also the live/dead marker will be essential in all of these analyses. ebioscience and biolegend have some good live/dead markers or you can use the traditional AAD if you are not planning to fix/perm your cells for intracellular staining.