The only strictly matching point is that it's a live action series involving kids pulled into a video game, and it's around the right timeframe, but could it be the 2003 Australian series, Pirate Islands?
Kate Redding, a sister of Nicholas and Sarah, is playing a new computer game called Pirate Islands, which has been created by her father. After Sarah tampers with the computer scanner, lightning strikes the house, and the scanner goes wild, zapping the three siblings inside the computer game. After teleporting inside the game, Kate meets Mars, the main character of the video game. Blackheart, the pirate captain, takes the siblings aboard the pirate ship and threatens to walk them off the plank, Mars climbs aboard and cuts the rope, causes the sails to fall against the pirates, the siblings escape and attempt to find their scanner, only to be cornered by the pirates and drop it into Blackheart's grasp, who uses it unknowingly to zap his crew-mate, causing him to pixelate and melt.
Kate discovers that users are transported between islands in the game through icons, after jumping inside, she ends up on castaway island only to find that Carmen, the second in command, has stolen all the items from Kate's bedroom. The pirates arrive and chase the gang off the island, causing Sarah to trip against a tree trunk which triggers a secret entrance inside the tree, which contains stairways up towards a hidden treehouse, the gang store their few belongings and decide to call this place their new home.
Nothing in the plot on Wikipedia mentions spelling out "help" with sticks, or getting a rubbing from a stone to discover engravings, but it seems like it would be within the genre.
Found by searching for tv series kids pulled into videogame -cartoon, which brought me to TV series about children ending up in father's computer game on this site.