No. If the "first hop" is between your unspecied model computer and the router via a wired ethernet connection, you have a broken CAT5 cable (or whatever else is between your computer and the DI-614+). If your "first hop" is between the router and your unspecified cable and DSL modem, it's the same problem in a different place. If your "first hop" is between your cable or DSL modem and the ISP's gateway, you have either a wiring/cable problem, or something that only the ISP can solve.
Since you're only using it for wired traffic the only reason to consider replacing it would be it's throughput. That is, if your uplink speed to the ISP has gotten faster then a new router might do a better job passing traffic. But if you're still behind, say, a DSL link then it might not matter. But beyond just bulk speed there's also session handling. Some routers do a markedly better job handling a lot of simultaneous traffic (well, it's all serialized packets, but I'm thinking more along the lines of lots of p2p traffic). For example, Verizon peddles an utter piece of crap Actiontec router for their new FIOS connections. The router is woefully bad at handling lots of sessions, so replacing it can help allow for better throughput. For Joe Sixpack just surfing the web and reading e-mail it probably won't matter though.
So it's really a matter of speed. There are various throughput testing tools out there. Some easier to configure than others. If you've got a good working knowledge of networking and have a couple of computers to spare you could setup a test network to put it through it's paces.
But it's likely there's nothing wrong with your current setup and no immediate reason to waste money replacing it.