You haven't given total details about what you mean when you say you installed "ASIO" a couple of years ago. There's no such thing as a generic ASIO driver--they're written specifically for the devices you wish to use.
ASIO4ALL is something a bit different. It takes the generic (MME) drivers as used by your built in sound card or Sound Blaster and makes them LOOK like ASIO to Reaper (or any other DAW). It's not true ASIO in that control is still by the MME drivers--it just gives you some ASIO controls of those MME drivers.
I think those who are suggesting a complete uninstall/reinstall are on the right track. Uninstall everything then install the current MME drivers for each of your devices and make sure they're working properly at that stage. Note that (assuming you're using Windows) you'll have to go to the Windows Sound Control panel and tell it to use either the built in or the Sound Blaster card as your default card. Each time you change, you have to do this twice--once for Record Devices and once for Playback devices.
I'm not
a Reaper user but I'll assume there's a set up screen where you tell it to either use MME or ASIO drivers and what sound devices to use. (Perhaps a Reaper user can help you with this.) Anyhow, get this working.
THEN re-install ASIO4ALL and set that to use/control the Sound Blaster. Set the Sound Blaster as your default device on both the Windows Sound (Record and Playback) screens--then tell Reaper to use ASIO4ALL as the driver and the Sound Blaster for recording and playback,
You should be able to get it going but I can see how a two year old ASIO driver for something floating around in your system could be causing problems.
At this point listen to the rubbish recordings the Sound Blaster will give and sell it.