my young elm tree has something eating it, keep it or not..?

out early this morning and found the tips, of what( looks like dead limbs )on half my elm tree,. had what appeared to be saw dust on top of each dead limb. i blew it off to expose a nice size hole right in the middle or core. sooo...i think it has a boring type bug .. so what i'd like to do is try and save what is left of the tree since half has leaves and growing fine..is this a lost cause or should i give it a try.. i planted three months ago after last real cold here in hominy ,oklahoma.none of the bored limbs have leaves so i figure if i cut off the bored limbs and spray (not been done) and don't like to do because of birds wildlife etc. with something, it might live .. i know it will probably be off balence and all but i'd like to keep it just for the shade it can provide..i am concerned for the other trees around it ,,mature walnut and 1yr flowering pear and 3month old peach and pear trees.
The walnut had worms with webs on it for two yaers and i sprayed it and this year it looks even better , no worms so far, wild birds , squirlles(?)long tail cute things, all love this tree now and so do i . I have mint and spearmint ,both growing around it's base.and the canopy is probably 15 feet wide this year.i tried english ivy to get it to grow up the tree (i love the look )but it seems to have maybe not faired the cold this last winter very well, i have a butterfly feeder there too.. yup, they like that too. this is the only tree on the property when we bought it 4 years ago and now i have my fig in back still small as the cold got it last winter too but it's growing from the base again, all tho, i lost two other figs out there, too cold naxt to the fence in shade there,so here's the list...
4 flowering pears
1 crab apple
3 figs-two died sorry haven't learned how to get pics from cam. to forum yet
2 peaches somtimes computors just scare me..been lurking around
1 elm daves for awhile never posted because don't know how, but
1 walnut this was really important.. hope you don't mind..no pic?

It might be saprophytic beetles eating what was already a dead limb. You really need to post a pic to help us out.

Go below where it says "Browse" and click there. That will take you to your hard drive. Navigate around your file system until you find the pic, highlight it by clicking once on it, and hit "open" and then hit "Preview." Give it a couple of minutes to load if you have a slow connection like mine, and try to keep the image size under 500K or so to make it easy for us to open. Then, if it's OK, hit "send."

Guy S.

hay thanks guy s.for the info all around I will try it within a couple of days to see if I can do it.(pics)I put miricle grow on it to help with the possible stress of the poor thing ,but thats all I've done .. tell I can figure what to do I'd hate to hack it to peices if somthing else can be done ,although your right the limbs seem to have been previously pruned by the nursery beforhand and do appear to be brittle too but there are green growing leaves on half the tree.. followup later with pics as soon as possible ok thanks again.. guy s.