I'm not sure about the PAE bit, but my old computer, retired last July, was a Pentium D, Intel's first dual core. I think it was basicly 2 P4s on the same die. I had only 1 Gb ram and a Geforce gt220 graphics card. This is the rig I first started running Linux on. I tried 3 different distros-Mint 13 cinnamon, Mageia 2, and Ultimate Edition 3.4 that also had compiz. They all worked and with the default Gallium graphics driver, not the better Nvidia driver. I don't know what you have for graphics, but if it is comparable to a gt220, I don't think you would have problems running any desktop. I knew my old computer was old and not very fast. I just didn't care. I wanted my desktop to look pleasing. What I tried did work reasonably with only 1Gb ram and a fairly low end graphics card.
I wouldn't add more ram. I'd stuff those few dollars into the piggy bank towards all new stuff later.
Also, I'm pretty sure the P4 supports PAE ( physical address extension ). I just don't remember, but I think the whole PAE thing has to do with 32 bit CPU's and the 4Gb ram limitation.
i5 3570k, ASRock z77 Extreme 4, 8 Gb Ripjaws 1600, Antec 430w psu, HVR 1600 tv tuner, custom case- marble top, oak face. Carver & DCM Time Window sound system. Mint 14 KDE.