Gas dryers are really pretty simple devices if you don't need to have the models with retracting fingers to fluff pillows and that special clothes-folding feature. :-)

Seriously, unless there is some feature (like sensor drying) that your Kenmore does not have that you really want, you may be best off either having someone look at your present dryer to figure out if it can be repaired economically, or you might just want to buy a dryer second-hand.

There are people who remodel and get rid of perfectly-serviceable appliances. I've done well buying used appliances from a trusted local independent appliance dealer. They've been refurbished by someone who knows how to fix them and they come with a warranty. I'm comfortable buying them because they'll scrap or cannibalize the ones which require too much work or are unlikely to last the warranty. I get 'em "like they used to build them" at a fair price, so it's a pretty decent deal.

Dryer about 10 - 15 years old? it's probably just the igniter.
It's not a hard repair and can be done by a handy home owner

Good point by Jakvis. Also check that your duct carrying the hot air from the dryer out of the house isn't clogged anywhere along the line, either with lint, or leaves (the louvers on the outside). People report remarkable improvement in drying time when duct is cleared out.

It's easy fix, it's the gas valve solenoid.
A Philip head screwdriver and 20 minuets is all it takes.

Here is a link that might be useful: gas valve solenoid