|"Pentium processors have inbuilt thermal overload protection. If it were overheating the outcome is a shutdown rather than a slowdown"|
Not exactly correct. 1st comes "throttling", which means the CPU speed will drop off in an attempt to lower the CPU temp....so initially, there would be a slowdown. However, if the temp continues to rise, the CPU will shutdown IF a certain trigger temp is reached.
"It's extremely slow but is fine in Safe Mode"
That's your clue. In Safe Mode, none of the background apps load, so I suspect there's some sort of malware/spware infection, possibly a virus. Boot into "normal" mode, hit Ctrl-Alt-Del to bring up Task Manager & check the CPU Usage...if the percentage is at or close to 100% at idle, try to determine what program is using it. You can run MSCONFIG from the start menu & see what listed under the startup tab, but you should also run a full virus & spyware scan.