Well... yes to RATTER15's suggestion, but only selectively. Most clibing roses (actually, it doesn't have the ability to "climb", as you've noted) produce the "abnormal" long canes... these long canes do not produce blooms but rather they bloom on "bloom stems" that emerge from the main canes or from secondary stems (called "laterals") growing out from these main canes. Both the main canes and the laterals are growth that has occurred during previous seasons. Therefore, it's important not to destroy the large canes, unless they are diseased, broken or otherwise damaged. Try to maintain four to 8 main canes if you can. Additionally, you say the rose has been there for several years, but keep in mind, for a true climber, remember the adage: First year sleeps, Second year creeps, Third year leaps! Patience is in order for at least 2 or 3 full growing seasons.
Lastly, only prune during the dormant season... late fall or very early spring. (Use a fertilizer with the middle number being the highest, by the way, don't overwater)... Best of luck!