I would like to remember a show from my childhood but only remember certain vague concepts from it. There was this girl, maybe a princess, who was kidnapped or trapped inside this machine (maybe her body was being used for some agenda??) and the main character of the story had to save her before it was too late. It could have easily been a mecha/monster show.
I remember wanting the main character to save her.
Sounds a bit like the opening two episodes / ending few episodes of Outlaw Star, which aired on Toonami.
In particular as that is how we are first introduced to Melfina, the living brain of the ship of the series (XGP15 / Outlaw Star), as she was being transported in a suitcase- it gets better. Melfina isn't really "trapped" in the ship, though she is captured a few times by the bad guys, and the final 4 or so episodes are a chase to save her.
Oh right, and the very last episode plays out somewhat like you remember with her being trapped someplace (a machine) and a "ticking clock" scenario, but I don't want to spoil it.
It could be "Full Metal Panic!".
The main characters are Kaname Chidori, a girl with a subconsciuos knowledge of advanced technologies (a "Whispered", as people with this power are called in the anime), and Sousuke Sagara, a boy (working for the covert agency Mithril) tasked with protecting her from terrorist organizations interested in her mysterious secrets.
In the fourth episode, Kaname is kidnapped and subjected to scientific testing, and Sousuke is sent to rescue her. This could be the episode you remember seeing.
Mechas (called "Arm Slaves" in the show) are used by both good guys and bad guys in the course of the series.
This anime originally ran in Japan in 2002 and was licensed for a North American release in 2003, so it fits your time frame.
