Hope this helps.
The IR for HDPE and LDPE is very similar. You should see three major sets of peaks. One set is at about 2950 recip cm-these don't give much information.
Typically, the polyethylenes have two more "doublets" (a doublet is a set of two very close, very sharp peaks) present that indicate crystallinity. The first doublet is in the range of 1450 recip cm. The second doublet is in the range of 800 recip cm (sorry, I'm at home and don't have the spectra in front of me, so the exact wavenumber may be different).
Some polyethylenes have low crystallinity. In these cases, the IR is very similar to that of mineral oil (usually called nujol). These peaks are broader. Some of the nujol like peaks, present because of low crystallinity, can also be in the crystalline polyethylene. This is where you should start.
LDPE uses free radical polymerization that has as a side-effect, something called "back biting". This causes a lot of 4 carbon length side chains on the LDPE polymer backbone.
Good luck with your lab.