Networking :: Best Way For Backing Up Availability Of Server?

At my work, we have an ISP that provides us with 2 connections with different IP addresses but at the moment they don't switch automatically if one fails, and can only work for outbound traffic.I tried to automate this with floating routing table on a CISCO 1711 router but then switching to the second link only happens when there's no longer a signal on the cable that's plugged into the router's interface directly -- and the failure most often happens somewhere in the middle. And that also does not make us available from outside.

Can anyone suggest a better way? Maybe an outside DNS server can have a second IP address recorded for our domain name?I found somewhere suggestions that a loadbalancer could solve that but these appliances are way too expensive.I also thought about using BGP but my router's RAM (128MB) is too small for the global routing table that BGP requires. And I also need an ISP (or better 2 ISPs) that provide BGP service. Before trying to convince others that we need to invest more into this, I'd like to know whether there are no easier ways.