In this paper, we analyse the coverage probability and the area spectral efficiency (ASE) for the uplink (UL) of dense small cell networks (SCNs) considering a practical path loss model incorporating both line-of-sight (LoS) and non-line-of-sight (NLoS) transmissions. Compared with the existing work, we adopt the following novel approaches in our study: (i) we assume a practical user association strategy (UAS) based on the smallest path loss, or equivalently the strongest received signal strength; (ii) we model the positions of both base stations (BSs) and the user equipments (UEs) as two independent Homogeneous Poisson point processes (HPPPs); and (iii) the correlation of BSs' and UEs' positions is considered, thus making our analytical results more accurate. The performance impact of LoS and NLoS transmissions on the ASE for the UL of dense SCNs is shown to be significant, both quantitatively and qualitatively, compared with existing work that does not differentiate LoS and NLoS transmissions. In particular, existing work predicted that a larger UL power compensation factor would always result in a better ASE in the practical range of BS density, i.e., 10^1-10^3 BSs/km^2. However, our results show that a smaller UL power compensation factor can greatly boost the ASE in the UL of dense SCNs, i.e., 10^2-10^3 BSs/km^2, while a larger UL power compensation factor is more suitable for sparse SCNs, i.e., 10^1-10^2 BSs/km^2.