With Painted Logs
In a situation like this all of the paint needs to be removed with either a chemical stripper or blasted with media (glass is most common now). The next step would be to cut out the rotted areas of wood and use Tim-bor or Boracol to saturate the logs and keep them from rotting any further. If the rotted areas are relatively shallow, LiquidWood can be used to seal cracks and create an undercoating for the WoodEpox to adhere to. Next, apply the WoodEpox and form it so that it conforms to the rest of the log. Dry pigment can be added to WoodEpox to color it (especially if you will be coating with a stain). Allow to dry thoroughly, then apply a new finish.
If large portions of the logs are rotted away, you will either have to replace portions of the log with half-log inserts or replace the entire log. You may need the services of a professional log home restoration contractor.
For DIY advice or restoration contractor referrals, call Schroeder Log Home Supply, Inc., at 1-800-359-6614 or contact electronically here.