If the peaks look like they have passed through a column ( with normal J reverse J peak profile and a decent peak width ), they are unlikely to be from the detector. If they are very sharp spikes or very very broad, they could be, but I very much doubt it.
I'd put a short ( 1-2m max ) thin-film, non-polar column between the injector and detector, reduce head pressure to obtain similar column flow, and perform some runs. If the peaks are still appearing ( will elute at earlier time/temperature, and will be closer together ), I'd suspect your sample solvent and/or injector.
What style is your glass inlet liner?, is it straight through, or have quartz wool, cup, or packing?. After reasonable use, is there much amber/black gunge on the liner.
What are your samples, do they contain derivatising reagents, and are there mono, di, triglycerides and/or sterols also present?. If you are injecting derivatising reagent, you could be reacting with non-volatile material from earlier samples in the injector and column, in which case you're probably doomed

. But you would need to solve the problem before subjecting your new column to the samples, and trying a short column should indicate whether the problem is the injector and/or column.
Sorry there are so many questions, but we need to know what the contamination looks like, and where the peaks fit in your normal profile.
Sterols tend to give large single peaks, MAGs and DAGs give couplets a couple of carbon numbers apart, and TAGs give multiple, overlapping, peaks a couple of carbons apart. All will be broader if they come from earlier injections and less obvious if from reactions on the column or injector.
Please keep having fun,
Bruce Hamilton