This does all sound a bit dark ages. At the very least your hosting company should look at switching you to a virtual server. Running that on highly resilient shared infrastructure would mitigate against pretty much any hardware fault from single component to whole physical server. This would also be more cost effective for the company in question in terms of running costs (cooling, power, rack space, support likelihood etc etc.)
And, as you mention, cloud is the obvious destination here (which in practical terms is the same as the above but on an industrial scale with the economies of scale that brings). AWS would have sizing/costing tools for IaaS which would include database estimations. Is it worth simply running one of those to get an initial idea?
But a 10 year old physical server sitting in a data centre, slowly popping it’s bits and relying on graveyard extractions for ongoing survival - You don’t need me to tell you that isn’t a long term solution.