Well that link is great to clean up a pc, however, if this computer that requires speeding up is proprietary,, then you need to do a bit of work,,
IBM now LENOVO is notorious for putting bog-down crap onto their pc's and notebooks!
You may need to delete all the "free" software to "free" you pc's processor time at boot.
check through Add/Remove and find out what all the progs are doing at startup,,
delete those annoying, useless little apps,, and you should see some boost in speed,,
plus,, d/l and install Bootvis, and let it optimize your boot process,,great little app,,
cheers