+1 on changing up the handlebar configuration. Not only can the new positions relieve the discomfort, a new style of handlebar on an old bike can bring new life into the bike and the riding experience!

On a straight or riser handlebar, some bar-ends are relatively cheap (sub-$20) and can be purchased at bike shops, online,[1] and I've even seen them by Bell Sports or Pacific Cycle/"Schwinn" at Walmarts around here. So that probably would be the cheapest route. You can even experiment by taking off the grips/brakes and moving these 'bar-end' pieces further inward on the bar (or have a close 'inner' and a farther-apart 'outer' pair to double the amount of new hand positions). If you keep them on the ends of the bars, you can also rotate them more skyward, or ground-ward but pointed toward you ('under' the handlebar); there are lots of options with those things!

Alternatively, switching up to a drop handlebar or a bullhorn/time-trial handlebar can make a huge difference as they bring your hands inward and allow for more sensitive steering, as well as offering more hand positions, including the vertical outside positions, which feel much more natural (in my opinion) than the 'bar-bell' position of a straight/riser bar. Beware that you may be tempted to raise your seat and assume a more aggressive riding posture if you switch to drop bars, though, which could cause you to put more weight on your hands and increase the discomfort. If you maintain a more upright position, however, these bars should increase your comfort overall.

Decent aluminum drop handlebars can be purchased for less than $10,[2] but you'd also probably need to purchase new brake levers (starting sub-$20[3][4]) and shifters if you didn't want the setup to look goofy. Bullhorns are available from around $25,[5] and a decent pair of brake levers for those start out around $20-25.[6]

On all types of handlebars, there are usually standard types of brakes and shifters and some more obscure and less-common options, like mountain-style brake levers used on drop-bars on cyclocross bikes and drop-bar- and stem- shifters for non-handlebar shifting. Depending on your current handlebar diameter you may be able to reuse your existing brakes and/or shifters. I'd measure your handlebar diameter or have a bike shop do it if you're unsure, and look for a handlebar with the same diameter if you want to go this route while saving money. Be aware that if you go with a non-standard kind of braking/shifting setup, though, you may not get the full experience-benefit/joy there is to be had from the new type of handlebar.

[1] http://www.jensonusa.com/store/produ...+Bar+Ends.aspx
[2] http://www.jensonusa.com/store/produ...+Road+Bar.aspx
[3] http://www.jensonusa.com/store/produ...ke+Levers.aspx
[4] http://www.jensonusa.com/store/produ...ke+Levers.aspx
[5] http://www.jensonusa.com/store/produ...um+Bar+09.aspx
[6] http://www.jensonusa.com/store/produ...ke+Levers.aspx