The closest you will come to that, at least from a reliable hosting company, is probably from OVH.com. They are infrastructure only though and don't support anything other than the hardware and their network. They will not even log into your server and don't even keep the logins once they email it to you.
Computer server rental | Start now for $49 - OVH
$109 for
Xeon 4 cores
4 TB SATA
64 GB RAM
500 Mbps unmetered with a burst of 1 Gbps
No SSD and no admin though, but you have way more bandwidth, RAM, and disk space.
With that much RAM you can keep your DB entirely in memory the whole time so SSD won't be needed.