Two immediate possibilities - is it making a whining type noise when it is running or actually firing - if so the chances are the oil pump has turned up its toes - it is possible to replace this component, a replacement requires the use of a high pressure flexible oil line and a suitable 1/8 inch socket coupler to run to the burner. If you are not familiar with how to set up an oil burner, don't do it yourself - you need to set pressures and check combustion - equipment needed for this. Second possibility is a blocked, or partially blocked, oil nozzle - again can be changed if you know what you are doing, but do not try unless you are confident. Always ensure you have observed all safety precautions necessary, together with ideally wearing suitable gloves, when working on any oil fired equipment - last thing you want to do is either burn your house down or develop a skin rash! Both of these events will outweigh the costs of going to a professional to do the work!
Jeremy, A Professional!, March 2009