You have a 2004 tow vehicle, but didn't mention the model year of your trailer.
[Edit - I see that you have edited your signature line to show that it is a 2001. That's a good thing for everyone to do.] In 2002 and before, you couldn't get at the power cord while the TM was closed. In 2004, TM had a design change, and you could. I'm not sure which way the 2003s were built.
On my 2006, the power cord is accessible through a hatch in the end of the bumper assembly. Since you can't do this, I assume you have a 2002 or older TM. Assuming this is true, you need to beware of one thing. In those years, the TM was equipped with a Magnetek Parallax 6300-series converter. The battery charger in this converter will happily overcharge your battery if you plug it in and leave it on for a couple weeks. Smart chargers were invented later, and later TMs have a smart converter from American Enterprises or WFCO.
In your case, you might do well to buy a small smart charger from Guest Industries and attach it to the TM electrical system via the Bargman connector that normally connects to your tow vehicle. I bought a model 2610 three-stage marine battery charger from Guest Industries on eBay afew years back. There are several Guest marine chargers on eBay right now, for very reasonable prices. For more info on these, go to
www.marinco.com, click "Battery Chargers", then click "Trolling Motor Chargers". The info you want will be under either "Single Battery" or "Dual Battery".
Bill