I have an ancient Dell Inspiron 710M which is still running. I want to hang onto it as I have some applications which will not run on Windows 10. I hear a lot of stories about failing lithium batteries causing fires. I guess batteries like most things break down over time. The battery only runs the laptop for ~15 minutes. Can I please seek some advice on whether the lithium battery is safe to continue using or should I dispose of the battery to be safe?
Unless the battery is showing signs of overheating, it's likely fine. Older batteries like the one in your system are steel-encased. The bigger issue is in newer systems which, due to slim form factors and weight, are no longer cased in steel - these can swell and cause issues ranging from sticky touchpads to physical damage to the system case as a result. Yours will not - older batteries are also under less stress as they're not subject to the same power demands and environments as hot as in newer systems.