Hi,
I'm an experienced sysadmin/developer (please check my reviews: 5 stars with 100% completion rate)..
I have computer science degree + specialization in web engineering and over 14 years' experience with web development..
It's hard to estimate time and cost without prior knowledge from your system, I would need to check it first.
Maybe your apache and/or mysql are incorrectly setup, maybe there's an issue on your theme or plugins, maybe something else is overloading your server (cron jobs or got hacked), there could be many reasons.. so time and cost depends..
but I can help you with this (and any other webdevelopment project you need).
If you're interested, please contact me so we can discuss details.
Thanks for your time