Yes you can, the clean up may not take long, the defragment may take longer.
But I doubt either will make much difference to the performance.
Dont confuse your laptop with being slow and your broadband being slow. Some people think if their broadband is slow it must be their laptop, which is not the case.
Check your broadband speed and see if it is what you are paying for.
1) Uninstall all programs you KNOW you dont want any more (dont uninstall anything if you dont know what it is).
2) Try to STOP programs starting up when the computer starts up if you dont need them. Each program that autostarts uses up memory and the more full your memory is the slower your computer can get.
3) Make sure there is plenty of real (RAM) memory. Nowadays 2Gb is probably a minimum.
4) Make sure there is plenty of room on your hard disk.
5) Run the free version of Malwarebytes to make sure you have no malware or spyware on your PC.