How come website be random slow? Open sleep processes?
IMHO,reason can be one of the following

i) Inline query :It is prone to sql injection attack.but not necessarily website will be slow.It is Advisable to use parameterise proc.

ii) Unpotimize query : Yes.shortlist those page and related query/proc.

iii) CSRF Attack : your pages can be attack by malware or web crawler.There are various way to overcome it,one of them is Captcha, but not always.google it.

iv) Network/server configuration :this should point i).check with your admin.

v) check for infinite and uncessary loop in pages.Infact identiyfy pages which are slow then examine both code and query.