Either way, without a HDMI port, the TV won't be able to dish out the 1080p quality that a HDMI port offers (as far as I'm aware, anyway). You can purchase something called a HDMI to AV converter, but obviously that won't give you 1080p quality. There are a few different types of "HD", which your TV's name could be referring to any of them. If there's no HDMI port, it's usually talking about 720p or 1080i (image will be upscaled but a bit blurry), but not that sharp 1080p that a HDMI cable and port offers you.
A Wii U has AV ports anyway so you don't need a converter in the first place. And running the HDMI cable into a converter and an AV cable from the converter to the TV will do the exact same thing as a direct AV link between the Wii U and the TV.
Some monitors come with a DVI port that is also capable of giving 1080p quality, but I doubt your TV/monitor would have such a thing because DVI does not give sound output. And a TV without sound is a useless TV.
If a real tech nerd could correct me/back me up on this, that'd be neat.
tl;dr - If I'm correct... No HDMI port = No 1080p for your Wii U on that particular TV/monitor, sadly.