I'd probably still search for any log, dmp or mdmp file extensions during that time. It could be a lot of things and with only getting one entry in the event log when the crashes happen, it won't be too easy to figure out. I'd also keep track of what you see logged before the crash.
It's looks like it's heap corruption of some sort which can sometimes happen with linked servers - usually old or faulty drivers though.
And if the backup agent was installed that could possibly be the issue even if there weren't any backups running.
There a way to monitor heap corruption but if you aren't getting any dump files, that would be pointless.

Seems the only thing you could do for now and with the crashes being fairly consistent with just the two changes to the server, I'd try uninstalling the backup agent and get rid of the linked servers for now.

Sue