Measuring glass transition temperatures by DSC can be challenging. I don't know much about DSC of PMMA in particular, but I do know that picking out the glass transition by DSC - which can often be a tiny little sigmoidal feature - requires a nice flat baseline, and the baseline here is kind of a mess. There are some specialized modes (they have different names depending on the instrument manufacturer sometimes - like modulated DSC) that are supposed to help deconvolute the glass transition features from, e.g., relaxation heating transitions that can be a problem in old samples. Bear in mind that DSC isn't really a fingerprint technique - the size and shape of transitions can depend quite a bit on input parameters like heating and cooling rates. Use the wrong heating/cooling rate, and you may not see the glass transition at all. It is not necessarily surprising that you aren't seeing what you're looking for based on a single scan acquired by a different operator.
The melting transition will be a large endotherm. But you haven't indicated which direction in the exothermic direction (or, for that matter, the temperature units), so it's not possible to tell.