What does your supply rail to the CC2540 look like when the GPRS module is running? if its clean I would expect either a pin conflict on the module to mcu interface or stray RF. How close is the antenna to the MCU and is it well matched? GPRS peak output is up to 2W so it can play havoc with unshielded and unfiltered signals. How long are your crystal traces? You need to put 33-47pf caps everywhere and bury most of your signals under ground plane if you can i.e. 4+ layer PCB.
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